A GPU ACCELERATED NODAL DISCONTINUOUS GALERKIN SOLVER FOR THE SOLUTION OF LATTICE-BOLTZMANN EQUATIONS ON UNSTRUCTURED MESHES

Date

2022-05-27

Author

Karakuş, Ali

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

91
views

0
downloads

We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Lattice-Boltzmann equations on unstructured triangular and quadrilateral meshes. The equations are discretized in time using semi-analytic time integration scheme enabling higher CFL numbers in stiff regimes. Performance portability of the solver on different platforms is achieved by using the open concurrent compute abstraction, OCCA. We optimize the performance of the most time-consuming kernels by tuning the fine-grain parallelism, memory utilization, and maximizing bandwidth. Accuracy and performance of the method are tested using distinct numerical cases including Couette flow, isothermal vortex and flow around square cylinder test cases. Preliminary numerical results confirm we achieve the design order accuracy in time and space.

URI

https://hdl.handle.net/11511/98435

Conference Name

Parallel Computational Fluid Dynamics

Collections

Department of Mechanical Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

A quadtree-based adaptively-refined cartesian-grid algorithm for solution of the euler equations Bulkök, Murat; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2005) A Cartesian method for solution of the steady two-dimensional Euler equations is produced. Dynamic data structures are used and both geometric and solution-based adaptations are applied. Solution adaptation is achieved through solution-based gradient information. The finite volume method is used with cell-centered approach. The solution is converged to a steady state by means of an approximate Riemann solver. Local time step is used for convergence acceleration. A multistage time stepping scheme is used to ...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
A two dimensional euler flow solver on adaptive cartesian grids Siyahhan, Bercan; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2008) In the thesis work, a code to solve the two dimensional compressible Euler equations for external flows around arbitrary geometries have been developed. A Cartesianmesh generator is incorporated to the solver. Hence the pre-processing can be performed together with the solution within a single code. The code is written in the C++ programming language and its object oriented capabilities have been exploited to save memory in the data structure developed. The Cartesian mesh is formed by dividing squares succe...
Development of discontinuous galerkin method 2 dimensional flow solver Güngör, Osman; Özgen, Serkan; Department of Aerospace Engineering (2019) In this work, 2 dimensional ﬂow solutions of Euler equations are presented from the developed discontinuous Galerkin method ﬁnite element method (DGFEM) solver on unstructured grids. Euler equations govern the inviscid and adiabatic ﬂows with a set of hyperbolic equations. The discretization of governing equations for DGFEM is given in detail. The DGFEM discretization provides high order solutions on an element-compact stencil hence only elements having common boundary are coupled. The required elementwise ...
A local discontinuous Galerkin method for Dirichlet boundary control problems Yücel, Hamdullah (null; 2018-10-20) In this paper, we consider Dirichlet boundary control of a convection-diffusion equation with L 2 4 – 5 boundary controls subject to pointwise bounds on the control posed on a two dimensional convex polygonal domain. 6 We use the local discontinuous Galerkin method as a discretization method. We derive a priori error estimates for 7 the approximation of the Dirichlet boundary control problem on a polygonal domain. Several numerical results are 8 provided to illustrate the theoretical results.

Citation Formats

A. Karakuş, “A GPU ACCELERATED NODAL DISCONTINUOUS GALERKIN SOLVER FOR THE SOLUTION OF LATTICE-BOLTZMANN EQUATIONS ON UNSTRUCTURED MESHES,” presented at the Parallel Computational Fluid Dynamics, Turin, İtalya, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/98435.