This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
A technique for analyzing dispersion properties of numerical schemes is proposed. The method is a... more A technique for analyzing dispersion properties of numerical schemes is proposed. The method is able to deal with both non dispersive or dispersive waves, i.e. waves for which the phase speed varies with wavenumber. It can be applied to unstructured grids and to finite domains with or without periodic boundary conditions. We consider the discrete version L of a linear differential operator L. An eigenvalue analysis of L gives eigenfunctions and eigenvalues (l i , λ i). The spatially resolved modes are found out using a standard a posteriori error estimation procedure applied to eigenmodes. Resolved eigenfunctions l i 's are used to determine numerical wavenumbers k i 's. Eigenvalues' imaginary parts are the wave frequencies ω i and a discrete dispersion relation ω i = f (k i) is constructed and compared with the exact dispersion relation of the continuous operator L. Real parts of eigenvalues λ i 's allow to compute dissipation errors of the scheme for each given class of wave. The method is applied to the discontinuous Galerkin discretization of shallow water equations in a rotating framework with a variable Coriolis force. Such a model exhibits three families of dispersive waves, including the slow Rossby waves that are usually difficult to analyze. In this paper, we present dissipation and dispersion errors for Rossby, Poincaré and Kelvin waves. We exhibit the strong superconvergence of numerical wave numbers issued of discontinuous Galerkin discretizations for all families of waves. In particular, the theoretical superconvergent rates, demonstrated for a one dimensional linear transport equation, for dissipation and dispersion errors are obtained in this two dimensional model with a variable Coriolis parameter for the Kelvin and Poincaré waves.
The intensive use of immersed granular flows has motivated a large amount of work in this field o... more The intensive use of immersed granular flows has motivated a large amount of work in this field of research. We present here a new numerical model to represent accurately and efficiently mixtures of fluid with grains. On one hand, the motion of the grains is solved at the grain scale by a contact dynamics method that consider grains as discrete elements. On the other hand, the fluid flow is computed from a continuous model of the mixture at a greater scale. The link between the two scales is provided by an interaction force based on the Darcy's law for porous media and used as a closure relation in the equations of the model. Some results of simulations in a two dimensional space are provided to prove the efficiency of the implementation.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
This paper describes an online coupling between a 3D discontinuous Galerkin finite element marine... more This paper describes an online coupling between a 3D discontinuous Galerkin finite element marine model and a 1D vertical turbulence closure model based on finite differences. The coupling exploits the topology of the 3D mesh, that is formed by stacking layers of prisms in the vertical direction. A robust mapping between the finite difference grid and the finite element function space is designed, taking into account the discontinuities in the latter. The coupling is tested with two horizontally homogeneous flows and an idealised 3D estuary simulation. The results are in good agreement with those obtained with a finite difference model using the same turbulence closure, indicating that the coupling does not deteriorate the performance of the turbulence model.
Computer Methods in Applied Mechanics and Engineering, Sep 1, 1996
Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order fin... more Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order finite element techniques fail to converge when the elasticity of the fluid is increased. In this paper, an adaptive hp-finite element method is used to solve differential viscoelastic flow problems. An a posteriori error estimator, based on some recent rigorous results of Oden and Wu for the Navier-Stokes equations ([1]) is also used. Starting from an initial mesh, local refinements (h-adaptivity) or enrichments (p-adaptivity) are applied in the spirit of the strategy proposed in [2]. The approximation error is reduced to a given level of accuracy with a minimal set of additional degrees of freedom. Numerical results on two 2D model problems illustrate both the validity of the error estimator presented and the efficiency of the adaptive procedure.
We discuss the basics of discontinuous Galerkin methods (DG) for CEM as an alternative of emergin... more We discuss the basics of discontinuous Galerkin methods (DG) for CEM as an alternative of emerging importance to the widely used FDTD. The benefits of DG methods include geometric flexibility, high-order accuracy, explicit timeadvancement, and very high parallel performance for large scale applications. The performance of the scheme shall be illustrated by several examples. As an example of particular interest, we further explore efficient probabilistic ways of dealing with uncertainty and uncertainty quantification in electromagnetics applications. Whereas the discussion often draws on scattering applications, the techniques are applicable to general problems in CEM.
This paper is devoted to the investigation of the density sorting of grains using water jigging. ... more This paper is devoted to the investigation of the density sorting of grains using water jigging. Experiments achieved in a laboratory scale water jig for two initial binary bed configurations are studied and compared to numerical results. The vertical composition of the deposit is estimated after different number of water pulses to represent the sorting evolution in time. Simulations are based on a multiscale model in which the fluid is solved at a larger scale than the grain diameter using the finite element method, while the grains are considered as rigid bodies and solved using the nonsmooth contact dynamics. Key parameters are numerically varied and observed to determine the sensitivity of the process.
We present a new modeling framework for sea-ice mechanics based on elasto-brittle (EB) behavior. ... more We present a new modeling framework for sea-ice mechanics based on elasto-brittle (EB) behavior. The EB framework considers sea ice as a continuous elastic plate encountering progressive damage, simulating the opening of cracks and leads. As a result of long-range elastic interactions, the stress relaxation following a damage event can induce an avalanche of damage. Damage propagates in narrow linear features, resulting in a very heterogeneous strain field. Idealized simulations of the Arctic sea-ice cover are analyzed in terms of ice strain rates and contrasted to observations and simulations performed with the classical viscous-plastic (VP) rheology. The statistical and scaling properties of ice strain rates are used as the evaluation metric. We show that EB simulations give a good representation of the shear faulting mechanism that accommodates most sea-ice deformation. The distributions of strain rates and the scaling laws of ice deformation are well captured by the EB framework, which is not the case for VP simulations. These results suggest that the properties of ice deformation emerge from elasto-brittle ice-mechanical behavior and motivate the implementation of the EB framework in a global sea-ice model.
In this paper, we show that one of the most widely used methods to solve the non-linear viscous-p... more In this paper, we show that one of the most widely used methods to solve the non-linear viscous-plastic (VP) sea ice rheology, the elastic-viscous-plastic (EVP) method, generates artificial linear bands of high deformation that may be confounded with real linear kinematic features observed in the Arctic ice pack. These numerical artefacts are easily filtered out by using a slightly different regularization of the internal stress. In addition, the EVP method is reinterpreted as an iterative solver and a clear distinction appears between the numerical and physical parameters. Two numerical parameters determine the stability and accuracy of the method and are adjusted to avoid the noisy ice deformation fields frequently observed with the EVP method in nearly rigid ice areas. This study also confirms the unsatisfactory numerical convergence of the EVP method and investigates the effects of the numerical parameters on sea ice deformation, internal stress and velocity fields obtained with unconverged solutions.
Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has represent... more Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. In this lagrangian version of the model, the computational ...
In recent years, unstructured-mesh models have gained attention due to their flexibility in repre... more In recent years, unstructured-mesh models have gained attention due to their flexibility in representing complex topography and variable spatial resolution. The Second generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim) is an unstructured-mesh finite element model that is being developed at the Universite catholique de Louvain (Louvain-la-Neuve, Belgium). The ocean model solves the shallow water equations by means of the discontinuous Galerkin finite element method. It features a 1D river model, 2D depth averaged model and a full 3D model. After a general presentation of SLIM and its main applications, we will further focus on sea-ice modeling. The sea-ice component of SLIM has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. Such an example is illustrated by the numerous narrow straits constituting the Canadian Arctic Archipelago. A key point of unstructured meshes is that they allow the use of mesh adaptivity. A Lagrangian, adaptive sea ice model allowing the computational grid to move with the ice drift is currently being developed. In order to maintain a good quality of the mesh, the mesh has to be adapted during the simulation, involving particular mesh adaptation techniques. This Lagrangian version of the model has several interesting applications, such as the dynamical mesh refinement along any region of interest (e.g., the ice edge), buoys tracking, or the inclusion of material properties in the rheology. Among these applications, the ice age constitutes both an interesting diagnostic tool and parameter for determining the ice physical properties (albedo, strength, salinity, ...). There are basically two ways of modeling the ice age: as a bidimensional tracer or as a vertical tracer, but different definitions exist and lead to different interpretations. In this work, we first present the equation of evolution of the age in an onedimensional ice layer. This equation is applied to a stand-alone thermodynamic sea ice model and its numerical resolution is compared to the integration of the ice age thanks to Lagrangian particles in the vertical direction. Preliminary results of a simulation of the Arctic Basin are finally shown where the Lagrangian model is used to transport the vertical structure of ice age
The FELIM model is being developed in the scope of the Second generation Louvainla-Neuve Ice-ocea... more The FELIM model is being developed in the scope of the Second generation Louvainla-Neuve Ice-ocean Model project (SLIM, www.climate.be/slim). This sea ice model has representations of both dynamic and thermodynamic sea ice processes and includes a viscous-plastic rheology formulation along with parameterizations of the atmospheric fluxes. The dynamical equations are written in a local, element-based coordinate system solving the problem of the singularity at the poles arising when the mesh is based on a geographical coordinate system (Comblen et al., 2009). The numerical resolution of this set of equations involves the standard Galerkin formulation and a Newton iterative procedure.
The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals wi... more The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals with the equations governing sea-ice, geophysical, environmental and groundwater phenomena by means of the (discontinuous Galerkin) finite element method on 1D, 2D or 3D unstructured meshes. To take advantage of state-of-the-art developments, SLIM is also being interfaced with existing tools (often based on radically different numerical methods), such as the well-known and widely used General Ocean Turbulence Model (www.gotm.net, GOTM). The post-processing of the results is achieved with the help of usual statistical and computer graphics methods. Other techniques are also resorted to, such as tracer and timescale methods derived from CART (Constituent-oriented Age and Residence time Theory, www.climate.be/cart) or network science tools (sites.uclouvain.be/networks) (Thomas et al. 2014).The hydrodynamics simulated by the aforementioned finite element model can be introduced into a number of SLIM-based environmental modules, which are capable of representing sediment transport (Delandmeter et al. 2015), as well as the fate of some classes of contaminants, namely microbiological pollutants (de Brauwere et al. 2014), endocrine disrupting compounds, heavy metals (Elskens et al. 2014) or radionuclides. A simple ecological model is being developed, whose aim is to simulate the evolution of various species of phyto- and zoo-plankton (Naithani et al. 2016).
The collapse dynamics and runout of columns of elongated grains in two dimensions are numerically... more The collapse dynamics and runout of columns of elongated grains in two dimensions are numerically investigated in dry and immersed conditions, by means of an unresolved finite elements/discrete elements model. The elongated grains are modeled as rigid aggregates of disks. The column aspect ratio is systematically varied from 0.125 to 16 in order to span short and tall columns. To analyze the effect of the initial grain orientation, columns with an initial grain orientation that is either random or aligned with a given direction are both considered. Collapse dynamics, both in dry and immersed cases, are found analogous to that previously observed for circular grain columns, particularly with respect to the power law dependency for the runout as a function of the column aspect ratio. The effect of the fluid mainly results in a decrease of the runout distance. Interestingly, the collapse dynamics and runout are not significantly affected by the initial orientation of the grains, except maybe in the extreme case where the grains are all horizontally oriented, which geometrically prevents the collapse. Finally, a scaling based on the front propagation energy is proposed allowing one to unify the runout of short to tall and dry to immersed columns in a single description, regardless of the initial grain orientation.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
A technique for analyzing dispersion properties of numerical schemes is proposed. The method is a... more A technique for analyzing dispersion properties of numerical schemes is proposed. The method is able to deal with both non dispersive or dispersive waves, i.e. waves for which the phase speed varies with wavenumber. It can be applied to unstructured grids and to finite domains with or without periodic boundary conditions. We consider the discrete version L of a linear differential operator L. An eigenvalue analysis of L gives eigenfunctions and eigenvalues (l i , λ i). The spatially resolved modes are found out using a standard a posteriori error estimation procedure applied to eigenmodes. Resolved eigenfunctions l i 's are used to determine numerical wavenumbers k i 's. Eigenvalues' imaginary parts are the wave frequencies ω i and a discrete dispersion relation ω i = f (k i) is constructed and compared with the exact dispersion relation of the continuous operator L. Real parts of eigenvalues λ i 's allow to compute dissipation errors of the scheme for each given class of wave. The method is applied to the discontinuous Galerkin discretization of shallow water equations in a rotating framework with a variable Coriolis force. Such a model exhibits three families of dispersive waves, including the slow Rossby waves that are usually difficult to analyze. In this paper, we present dissipation and dispersion errors for Rossby, Poincaré and Kelvin waves. We exhibit the strong superconvergence of numerical wave numbers issued of discontinuous Galerkin discretizations for all families of waves. In particular, the theoretical superconvergent rates, demonstrated for a one dimensional linear transport equation, for dissipation and dispersion errors are obtained in this two dimensional model with a variable Coriolis parameter for the Kelvin and Poincaré waves.
The intensive use of immersed granular flows has motivated a large amount of work in this field o... more The intensive use of immersed granular flows has motivated a large amount of work in this field of research. We present here a new numerical model to represent accurately and efficiently mixtures of fluid with grains. On one hand, the motion of the grains is solved at the grain scale by a contact dynamics method that consider grains as discrete elements. On the other hand, the fluid flow is computed from a continuous model of the mixture at a greater scale. The link between the two scales is provided by an interaction force based on the Darcy's law for porous media and used as a closure relation in the equations of the model. Some results of simulations in a two dimensional space are provided to prove the efficiency of the implementation.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
This paper describes an online coupling between a 3D discontinuous Galerkin finite element marine... more This paper describes an online coupling between a 3D discontinuous Galerkin finite element marine model and a 1D vertical turbulence closure model based on finite differences. The coupling exploits the topology of the 3D mesh, that is formed by stacking layers of prisms in the vertical direction. A robust mapping between the finite difference grid and the finite element function space is designed, taking into account the discontinuities in the latter. The coupling is tested with two horizontally homogeneous flows and an idealised 3D estuary simulation. The results are in good agreement with those obtained with a finite difference model using the same turbulence closure, indicating that the coupling does not deteriorate the performance of the turbulence model.
Computer Methods in Applied Mechanics and Engineering, Sep 1, 1996
Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order fin... more Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order finite element techniques fail to converge when the elasticity of the fluid is increased. In this paper, an adaptive hp-finite element method is used to solve differential viscoelastic flow problems. An a posteriori error estimator, based on some recent rigorous results of Oden and Wu for the Navier-Stokes equations ([1]) is also used. Starting from an initial mesh, local refinements (h-adaptivity) or enrichments (p-adaptivity) are applied in the spirit of the strategy proposed in [2]. The approximation error is reduced to a given level of accuracy with a minimal set of additional degrees of freedom. Numerical results on two 2D model problems illustrate both the validity of the error estimator presented and the efficiency of the adaptive procedure.
We discuss the basics of discontinuous Galerkin methods (DG) for CEM as an alternative of emergin... more We discuss the basics of discontinuous Galerkin methods (DG) for CEM as an alternative of emerging importance to the widely used FDTD. The benefits of DG methods include geometric flexibility, high-order accuracy, explicit timeadvancement, and very high parallel performance for large scale applications. The performance of the scheme shall be illustrated by several examples. As an example of particular interest, we further explore efficient probabilistic ways of dealing with uncertainty and uncertainty quantification in electromagnetics applications. Whereas the discussion often draws on scattering applications, the techniques are applicable to general problems in CEM.
This paper is devoted to the investigation of the density sorting of grains using water jigging. ... more This paper is devoted to the investigation of the density sorting of grains using water jigging. Experiments achieved in a laboratory scale water jig for two initial binary bed configurations are studied and compared to numerical results. The vertical composition of the deposit is estimated after different number of water pulses to represent the sorting evolution in time. Simulations are based on a multiscale model in which the fluid is solved at a larger scale than the grain diameter using the finite element method, while the grains are considered as rigid bodies and solved using the nonsmooth contact dynamics. Key parameters are numerically varied and observed to determine the sensitivity of the process.
We present a new modeling framework for sea-ice mechanics based on elasto-brittle (EB) behavior. ... more We present a new modeling framework for sea-ice mechanics based on elasto-brittle (EB) behavior. The EB framework considers sea ice as a continuous elastic plate encountering progressive damage, simulating the opening of cracks and leads. As a result of long-range elastic interactions, the stress relaxation following a damage event can induce an avalanche of damage. Damage propagates in narrow linear features, resulting in a very heterogeneous strain field. Idealized simulations of the Arctic sea-ice cover are analyzed in terms of ice strain rates and contrasted to observations and simulations performed with the classical viscous-plastic (VP) rheology. The statistical and scaling properties of ice strain rates are used as the evaluation metric. We show that EB simulations give a good representation of the shear faulting mechanism that accommodates most sea-ice deformation. The distributions of strain rates and the scaling laws of ice deformation are well captured by the EB framework, which is not the case for VP simulations. These results suggest that the properties of ice deformation emerge from elasto-brittle ice-mechanical behavior and motivate the implementation of the EB framework in a global sea-ice model.
In this paper, we show that one of the most widely used methods to solve the non-linear viscous-p... more In this paper, we show that one of the most widely used methods to solve the non-linear viscous-plastic (VP) sea ice rheology, the elastic-viscous-plastic (EVP) method, generates artificial linear bands of high deformation that may be confounded with real linear kinematic features observed in the Arctic ice pack. These numerical artefacts are easily filtered out by using a slightly different regularization of the internal stress. In addition, the EVP method is reinterpreted as an iterative solver and a clear distinction appears between the numerical and physical parameters. Two numerical parameters determine the stability and accuracy of the method and are adjusted to avoid the noisy ice deformation fields frequently observed with the EVP method in nearly rigid ice areas. This study also confirms the unsatisfactory numerical convergence of the EVP method and investigates the effects of the numerical parameters on sea ice deformation, internal stress and velocity fields obtained with unconverged solutions.
Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has represent... more Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. In this lagrangian version of the model, the computational ...
In recent years, unstructured-mesh models have gained attention due to their flexibility in repre... more In recent years, unstructured-mesh models have gained attention due to their flexibility in representing complex topography and variable spatial resolution. The Second generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim) is an unstructured-mesh finite element model that is being developed at the Universite catholique de Louvain (Louvain-la-Neuve, Belgium). The ocean model solves the shallow water equations by means of the discontinuous Galerkin finite element method. It features a 1D river model, 2D depth averaged model and a full 3D model. After a general presentation of SLIM and its main applications, we will further focus on sea-ice modeling. The sea-ice component of SLIM has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. Such an example is illustrated by the numerous narrow straits constituting the Canadian Arctic Archipelago. A key point of unstructured meshes is that they allow the use of mesh adaptivity. A Lagrangian, adaptive sea ice model allowing the computational grid to move with the ice drift is currently being developed. In order to maintain a good quality of the mesh, the mesh has to be adapted during the simulation, involving particular mesh adaptation techniques. This Lagrangian version of the model has several interesting applications, such as the dynamical mesh refinement along any region of interest (e.g., the ice edge), buoys tracking, or the inclusion of material properties in the rheology. Among these applications, the ice age constitutes both an interesting diagnostic tool and parameter for determining the ice physical properties (albedo, strength, salinity, ...). There are basically two ways of modeling the ice age: as a bidimensional tracer or as a vertical tracer, but different definitions exist and lead to different interpretations. In this work, we first present the equation of evolution of the age in an onedimensional ice layer. This equation is applied to a stand-alone thermodynamic sea ice model and its numerical resolution is compared to the integration of the ice age thanks to Lagrangian particles in the vertical direction. Preliminary results of a simulation of the Arctic Basin are finally shown where the Lagrangian model is used to transport the vertical structure of ice age
The FELIM model is being developed in the scope of the Second generation Louvainla-Neuve Ice-ocea... more The FELIM model is being developed in the scope of the Second generation Louvainla-Neuve Ice-ocean Model project (SLIM, www.climate.be/slim). This sea ice model has representations of both dynamic and thermodynamic sea ice processes and includes a viscous-plastic rheology formulation along with parameterizations of the atmospheric fluxes. The dynamical equations are written in a local, element-based coordinate system solving the problem of the singularity at the poles arising when the mesh is based on a geographical coordinate system (Comblen et al., 2009). The numerical resolution of this set of equations involves the standard Galerkin formulation and a Newton iterative procedure.
The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals wi... more The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals with the equations governing sea-ice, geophysical, environmental and groundwater phenomena by means of the (discontinuous Galerkin) finite element method on 1D, 2D or 3D unstructured meshes. To take advantage of state-of-the-art developments, SLIM is also being interfaced with existing tools (often based on radically different numerical methods), such as the well-known and widely used General Ocean Turbulence Model (www.gotm.net, GOTM). The post-processing of the results is achieved with the help of usual statistical and computer graphics methods. Other techniques are also resorted to, such as tracer and timescale methods derived from CART (Constituent-oriented Age and Residence time Theory, www.climate.be/cart) or network science tools (sites.uclouvain.be/networks) (Thomas et al. 2014).The hydrodynamics simulated by the aforementioned finite element model can be introduced into a number of SLIM-based environmental modules, which are capable of representing sediment transport (Delandmeter et al. 2015), as well as the fate of some classes of contaminants, namely microbiological pollutants (de Brauwere et al. 2014), endocrine disrupting compounds, heavy metals (Elskens et al. 2014) or radionuclides. A simple ecological model is being developed, whose aim is to simulate the evolution of various species of phyto- and zoo-plankton (Naithani et al. 2016).
The collapse dynamics and runout of columns of elongated grains in two dimensions are numerically... more The collapse dynamics and runout of columns of elongated grains in two dimensions are numerically investigated in dry and immersed conditions, by means of an unresolved finite elements/discrete elements model. The elongated grains are modeled as rigid aggregates of disks. The column aspect ratio is systematically varied from 0.125 to 16 in order to span short and tall columns. To analyze the effect of the initial grain orientation, columns with an initial grain orientation that is either random or aligned with a given direction are both considered. Collapse dynamics, both in dry and immersed cases, are found analogous to that previously observed for circular grain columns, particularly with respect to the power law dependency for the runout as a function of the column aspect ratio. The effect of the fluid mainly results in a decrease of the runout distance. Interestingly, the collapse dynamics and runout are not significantly affected by the initial orientation of the grains, except maybe in the extreme case where the grains are all horizontally oriented, which geometrically prevents the collapse. Finally, a scaling based on the front propagation energy is proposed allowing one to unify the runout of short to tall and dry to immersed columns in a single description, regardless of the initial grain orientation.
Uploads
Papers by Vincent Legat