Modification of algebraic multigrid for effective GPGPU-based solution of nonstationary hydrodynamics problems

We present modification of algebraic multigrid algorithm for effective GPGPU-based solution of nonstationary hydrodynamics problems. The modification is easy to implement and allows us to reduce number of times when the multigrid setup is performed, thus saving up to 50% of computation time with respect to unmodified algorithm. © 2012 Elsevier B.V

Simulation of two- and three-dimensional viscoplastic flows using adaptive mesh refinement

This paper presents a finite element solver for the simulation of steady non-Newtonian flow problems, using a regularized Bingham model, with adaptive mesh refinement capabilities. The solver is based on a stabilized formulation derived from the variational multiscale framework. This choice allows the introduction of an a posteriori error indicator based on the small scale part of the solution, which is used to drive a mesh refinement procedure based on element subdivision. This approach applied to the solution of a series of benchmark examples, which allow us to validate the formulation and assess its capabilities to model 2D and 3D non-Newtonian flows.Postprint (author's final draft

Modification of algebraic multigrid for effective GPGPU-based solution of nonstationary hydrodynamics problems

We present modification of algebraic multigrid algorithm for effective GPGPU-based solution of nonstationary hydrodynamics problems. The modification is easy to implement and allows us to reduce number of times when the multigrid setup is performed, thus saving up to 50% of computation time with respect to unmodified algorithm. © 2012 Elsevier B.V

Modification of algebraic multigrid for effective GPGPU-based solution of nonstationary hydrodynamics problems

We present modification of algebraic multigrid algorithm for effective GPGPU-based solution of nonstationary hydrodynamics problems. The modification is easy to implement and allows us to reduce number of times when the multigrid setup is performed, thus saving up to 50% of computation time with respect to unmodified algorithm. © 2012 Elsevier B.V

Modification of algebraic multigrid for effective GPGPU-based solution of nonstationary hydrodynamics problems

We present modification of algebraic multigrid algorithm for effective GPGPU-based solution of nonstationary hydrodynamics problems. The modification is easy to implement and allows us to reduce number of times when the multigrid setup is performed, thus saving up to 50% of computation time with respect to unmodified algorithm. © 2012 Elsevier B.V

Lattice Boltzmann Methods for Partial Differential Equations

Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. To computationally analyze nonlinear stability, extensive numerical tests are enabled by combining the intrinsic parallelizability of lattice Boltzmann methods with the platform-agnostic and scalable open-source framework OpenLB. Through upscaling the number and quality of computations, large variations in the parameter spaces of classical benchmark problems are considered for the exploratory indication of methodological insights. Finally, the introduced mathematical and computational techniques are applied for the proposal and analysis of new lattice Boltzmann methods. Based on stabilized relaxation, limit consistent discretizations, and consistent temporal filters, novel numerical schemes are developed for approximating initial value problems and initial boundary value problems as well as coupled systems thereof. In particular, lattice Boltzmann methods are proposed and analyzed for temporal large eddy simulation, for simulating homogenized nonstationary fluid flow through porous media, for binary fluid flow simulations with higher order free energy models, and for the combination with Monte Carlo sampling to approximate statistical solutions of the incompressible Euler equations in three dimensions