Papers by Aditya Velivelli
Advances in Engineering Software, Apr 1, 2015
The lattice Boltzmann method (LBM) and traditional finite difference methods have separate stren... more The lattice Boltzmann method (LBM) and traditional finite difference methods have separate strengths when solving the incompressible Navier-Stokes equations. The LBM is an explicit method with a highly local computational nature that uses floatingpoint operations that involve only local data and thereby enables easy cache optimization and parallelization. However, because the LBM is an explicit method, smaller grid spacing requires smaller numerical time steps during both transient and steady state computations. Traditional implicit finite difference methods can take larger time steps as they are not limited by the CFL condition, but only by the need for time accuracy during transient computations. To take advantage of the strengths of both methods, a multiple solver, multiple grid block approach was implemented and validated for the 2-D Burgers' equation in Part I of this work. Part II implements the multiple solver, multiple grid block approach for the 2-D backward step flow problem. The coupled LBM-VSM solver is found to be faster by a factor of 2.90 (2.87 and 2.93 for Re = 150 and Re = 500, respectively) on a single processor than the VSM for the 2-D backward step flow problem while maintaining similar accuracy. c
Fluids Engineering, 2004
The use of the lattice Boltzmann method in computational fluid dynamics has been steadily increas... more The use of the lattice Boltzmann method in computational fluid dynamics has been steadily increasing. The highly local nature of lattice Boltzmann computations have allowed for easy cache optimization and parallelization. This bestows the lattice Boltzmann method with considerable superiority in computational performance over traditional finite difference methods for solving unsteady flow problems. When solving steady flow problems, the explicit nature of the lattice Boltzmann discretization limits the time step size. The time step size is limited by the Courant-Friedrichs-Lewy (CFL) condition and local gradients in the solution, the latter limitation being more extreme. This paper describes a novel explicit discretization for the lattice Boltzmann method that can perform simulations with larger time step sizes. The new algorithm is applid to the steady Burger’s equation, uux = μ(uxx + uyy), which is a nonlinear partial differential equation containing both convection and diffusion terms. A comparison between the original lattice Boltzmann method and the new algorithm is performed with regard to time for computation and accuracy.
SAE technical paper series, Apr 14, 2020
Advances in Engineering Software, Apr 1, 2014
The lattice Boltzmann method is being increasingly employed in the field of computational fluid d... more The lattice Boltzmann method is being increasingly employed in the field of computational fluid dynamics due to its computational efficiency. Floating-point operations in the lattice Boltzmann method involve local data and therefore allow easy cache optimization and parallelization. Due to this, the cache-optimized lattice Boltzmann method has superior computational performance over traditional finite difference methods for solving unsteady flow problems. When solving steady flow problems, the explicit nature of the lattice Boltzmann discretization limits the time step size and therefore the efficiency of the lattice Boltzmann method for steady flows. To quantify the computational performance of the lattice Boltzmann method for steady flows, a comparison study between the lattice Boltzmann method (LBM) and the alternating direction implicit (ADI) method was performed using the 2-D steady Burgers' equation. The comparison study showed that the LBM performs comparatively poor on high-resolution meshes due to smaller time step sizes, while on coarser meshes where the time step size is similar for both methods, the cache-optimized LBM performance is superior. Because flow domains can be discretized with multiblock grids consisting of coarse and fine grid blocks, the cache-optimized LBM can be applied on the coarse grid block while the traditional implicit methods are applied on the fine grid blocks. This paper finds the coupled cache-optimized lattice Boltzmann-ADI method to be faster by a factor of 4.5 over the traditional methods while maintaining similar accuracy.
Concurrency and Computation: Practice and Experience, Oct 12, 2004
The lattice Boltzmann method is an important technique for the numerical solution of partial diff... more The lattice Boltzmann method is an important technique for the numerical solution of partial differential equations because it has nearly ideal scalability on parallel computers for many applications. However, to achieve the scalability and speed potential of the lattice Boltzmann technique, the issues of data reusability in cache-based computer architectures must be addressed. Utilizing the two-dimensional diffusion equation, T t = µ(T xx + T yy), this paper examines cache optimization for the lattice Boltzmann method in both serial and parallel implementations. In this study, speedups due to cache optimization were found to be 1.9-2.5 for the serial implementation and 3.6-3.8 for the parallel case in which the domain decomposition was optimized for stride-one access. In the parallel non-cached implementation, the method of domain decomposition (horizontal or vertical) used for parallelization did not significantly affect the compute time. In contrast, the cache-based implementation of the lattice Boltzmann method was significantly faster when the domain decomposition was optimized for stride-one access. Additionally, the cache-optimized lattice Boltzmann method in which the domain decomposition was optimized for stride-one access displayed superlinear scalability on all problem sizes as the number of processors was increased.
Physica D: Nonlinear Phenomena, Mar 1, 2006
Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics du... more Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency. In order to quantify the computational efficiency and accuracy of the lattice Boltzmann method, it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme. The lattice Boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size. Due to this, data is obtained from the main memory and this access is much slower than access to cache memory. Using a cache-optimized lattice Boltzmann algorithm, this paper takes into account the full computational strength of the lattice Boltzmann method. The com parison is performed on both a single processor and multiple processors.
Concurrency and Computation: Practice and Experience, Dec 10, 2004
The lattice Boltzmann method is an important technique for the numerical solution of partial diff... more The lattice Boltzmann method is an important technique for the numerical solution of partial differential equations because it has nearly ideal scalability on parallel computers for many applications. However, to achieve the scalability and speed potential of the lattice Boltzmann technique, the issues of data reusability in cache-based computer architectures must be addressed. Utilizing the two-dimensional diffusion equation, T t = µ(T xx + T yy), this paper examines cache optimization for the lattice Boltzmann method in both serial and parallel implementations. In this study, speedups due to cache optimization were found to be 1.9-2.5 for the serial implementation and 3.6-3.8 for the parallel case in which the domain decomposition was optimized for stride-one access. In the parallel non-cached implementation, the method of domain decomposition (horizontal or vertical) used for parallelization did not significantly affect the compute time. In contrast, the cache-based implementation of the lattice Boltzmann method was significantly faster when the domain decomposition was optimized for stride-one access. Additionally, the cache-optimized lattice Boltzmann method in which the domain decomposition was optimized for stride-one access displayed superlinear scalability on all problem sizes as the number of processors was increased.
IGI Global eBooks, Apr 12, 2012
ABSTRACT Sign-based stigmergic methods such as the ant colony optimization algorithm have been us... more ABSTRACT Sign-based stigmergic methods such as the ant colony optimization algorithm have been used to solve network optimization, scheduling problems, and other optimization problems that can be visualized as directed graphs. However, there has been little research focused on the use of optimization methods based on sematectonic stigmergy, such as coordination through collective construction. This paper develops a novel approach where the process of agent-directed stigmergic construction is introduced as a general optimization tool. The development of this new approach involves adopting previous work on stigmergic construction to a virtual space and applying statistical mechanics-based techniques to data produced during the stigmergic construction process. From this a unique procedure for solving optimization problems using a computational procedure that simulates sematectonic stigmergic processes such as stigmergic construction is proposed.
SAE International journal of passenger cars, Mar 28, 2017
This paper presents the development of a virtual sculpting system, with the goal of enabling the ... more This paper presents the development of a virtual sculpting system, with the goal of enabling the user to create a freeform model by carving a virtual workpiece with a virtual tool while providing haptic interface during the sculpting process. A virtual reality approach is taken to provide stereoscopic viewing and force feedback, thus making the process of model creation in the virtual environment easier and more intuitive. The development of this system involves integrating techniques and algorithms in geometric modeling, computer graphics, and haptic rendering. Multithreading is used in an attempt to address the different update rates required in the graphic and haptic displays.
Fluids Engineering, 2003
... Aditya C. Velivelli, Kenneth M. Bryden. Abstract. ... Utilizing the two-dimensional diffusion... more ... Aditya C. Velivelli, Kenneth M. Bryden. Abstract. ... Utilizing the two-dimensional diffusion equation, , this paper examines the parallel performance for the lattice Boltzmann method and the alternating direction implicit (ADI) method. ...
Fluids Engineering, 2004
The use of the lattice Boltzmann method in computational fluid dynamics has been steadily increas... more The use of the lattice Boltzmann method in computational fluid dynamics has been steadily increasing. The highly local nature of lattice Boltzmann computations have allowed for easy cache optimization and parallelization. This bestows the lattice Boltzmann method with considerable superiority in computational performance over traditional finite difference methods for solving unsteady flow problems. When solving steady flow problems, the explicit nature of the lattice Boltzmann discretization limits the time step size. The time step size is limited by the Courant-Friedrichs-Lewy (CFL) condition and local gradients in the solution, the latter limitation being more extreme. This paper describes a novel explicit discretization for the lattice Boltzmann method that can perform simulations with larger time step sizes. The new algorithm is applid to the steady Burger’s equation, uux = μ(uxx + uyy), which is a nonlinear partial differential equation containing both convection and diffusion ...
SAE International Journal of Passenger Cars - Electronic and Electrical Systems, 2014
Manufacturing, 2002
This paper presents the development of a virtual sculpting system, with the goal of enabling the ... more This paper presents the development of a virtual sculpting system, with the goal of enabling the user to create a freeform model by carving a virtual workpiece with a virtual tool while providing haptic interface during the sculpting process. A virtual reality approach is taken to provide stereoscopic viewing and force feedback, thus making the process of model creation in the virtual environment easier and more intuitive. The development of this system involves integrating techniques and algorithms in geometric modeling, computer graphics, and haptic rendering. Multithreading is used in an attempt to address the different update rates required in the graphic and haptic displays.
45th AIAA Aerospace Sciences Meeting and Exhibit, 2007
The long term goal of our work is to enable rapid prototyping design optimization to take place o... more The long term goal of our work is to enable rapid prototyping design optimization to take place on geometries of arbitrary size in a spirit of a real time computer game. In recent papers we have reported the integration of a Level Set based geometry kernel with an octree-based cut-Cartesian mesh generator, RANS flow solver and post-processing all within a single piece of software - and all implemented in parallel with commodity PC clusters as the target. This work has shown that it is possible to eliminate all serial bottlenecks from the CED Process. This paper reports further progress towards our goal; in particular we report on the generation of viscous layer meshes to bridge the body to the flow across the cut-cells. The Level Set formulation, which underpins the geometry representation, is used as a natural mechanism to allow rapid construction of conformal layer meshes. The guiding principle is to construct the mesh which most closely approximates the body but remains solvable. This apparently novel approach is described and examples given.
International Journal of Agent Technologies and Systems, 2011
Sign-based stigmergic methods such as the ant colony optimization algorithm have been used to sol... more Sign-based stigmergic methods such as the ant colony optimization algorithm have been used to solve network optimization, scheduling problems, and other optimization problems that can be visualized as directed graphs. However, there has been little research focused on the use of optimization methods based on sematectonic stigmergy, such as coordination through collective construction. This paper develops a novel approach where the process of agent-directed stigmergic construction is introduced as a general optimization tool. The development of this new approach involves adopting previous work on stigmergic construction to a virtual space and applying statistical mechanics–based techniques to data produced during the stigmergic construction process. From this a unique procedure for solving optimization problems using a computational procedure that simulates sematectonic stigmergic processes such as stigmergic construction is proposed.
Advances in Engineering Software, 2014
The lattice Boltzmann method is being increasingly employed in the field of computational fluid d... more The lattice Boltzmann method is being increasingly employed in the field of computational fluid dynamics due to its computational efficiency. Floating-point operations in the lattice Boltzmann method involve local data and therefore allow easy cache optimization and parallelization. Due to this, the cache-optimized lattice Boltzmann method has superior computational performance over traditional finite difference methods for solving unsteady flow problems. When solving steady flow problems, the explicit nature of the lattice Boltzmann discretization limits the time step size and therefore the efficiency of the lattice Boltzmann method for steady flows. To quantify the computational performance of the lattice Boltzmann method for steady flows, a comparison study between the lattice Boltzmann method (LBM) and the alternating direction implicit (ADI) method was performed using the 2-D steady Burgers' equation. The comparison study showed that the LBM performs comparatively poor on high-resolution meshes due to smaller time step sizes, while on coarser meshes where the time step size is similar for both methods, the cache-optimized LBM performance is superior. Because flow domains can be discretized with multiblock grids consisting of coarse and fine grid blocks, the cache-optimized LBM can be applied on the coarse grid block while the traditional implicit methods are applied on the fine grid blocks. This paper finds the coupled cache-optimized lattice Boltzmann-ADI method to be faster by a factor of 4.5 over the traditional methods while maintaining similar accuracy.
Concurrency and Computation: Practice and Experience, 2004
The lattice Boltzmann method is an important technique for the numerical solution of partial diff... more The lattice Boltzmann method is an important technique for the numerical solution of partial differential equations because it has nearly ideal scalability on parallel computers for many applications. However, to achieve the scalability and speed potential of the lattice Boltzmann technique, the issues of data reusability in cache-based computer architectures must be addressed. Utilizing the two-dimensional diffusion equation, T t = µ(T xx + T yy), this paper examines cache optimization for the lattice Boltzmann method in both serial and parallel implementations. In this study, speedups due to cache optimization were found to be 1.9-2.5 for the serial implementation and 3.6-3.8 for the parallel case in which the domain decomposition was optimized for stride-one access. In the parallel non-cached implementation, the method of domain decomposition (horizontal or vertical) used for parallelization did not significantly affect the compute time. In contrast, the cache-based implementation of the lattice Boltzmann method was significantly faster when the domain decomposition was optimized for stride-one access. Additionally, the cache-optimized lattice Boltzmann method in which the domain decomposition was optimized for stride-one access displayed superlinear scalability on all problem sizes as the number of processors was increased.
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Papers by Aditya Velivelli