ALI KARAKUS

GPU ACCELERATION OF A HIGH-ORDER DISCONTINUOUS GALERKIN BASED INCOMPRESSIBLE FLOW SOLVER.

December, 2017

Authors: Ali Karakus, Noel Chalmers, Kasia Swirydowicz  and Tim Warburton

Submitted to Computers and Fluids

Abstract: We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier–Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of the nonlinear term and implicit treatment of the split Stokes operators. The pressure system is solved with a conjugate gradient method together with a fully GPU-accelerated multigrid preconditioner which is designed to minimize memory requirements and to increase overall performance. A semi-Lagrangian subcycling advection algorithm is used to shift the computational load per timestep away from the pressure Poisson solve by allowing larger timestep sizes in exchange for an increased number of advection steps. Numerical results confirm we achieve the design order accuracy in time and space. We optimize the performance of the most time-consuming kernels by tuning the fine-grain parallelism, memory utilization, and maximizing bandwidth. To assess overall performance we present an empirically calibrated roofline performance model for a target GPU to explain the achieved efficiency. We demonstrate that, in the most cases, the kernels used in the solver are close to their empirically predicted roofline performance.

AN ADAPTIVE FULLY DISCONTINUOUS GALERKIN LEVEL SET METHOD FOR INCOMPRESSIBLE MULTIPHASE FLOWS.

Accepted. August, 2017

Authors: Ali Karakus, Tim Warburton,  Haluk Aksel and Cuneyt Sert

Journal: International Journal of Numerical Methods for Heat & Fluid Flow

Abstract: This study focuses on the development of a high-order discontinuous Galerkin method for the solution of unsteady, incompressible, multiphase flows with level set interface formulation. Nodal discontinuous Galerkin discretization is used for incompressible Navier-Stokes, level set advection and reinitialization equations on adaptive unstructured elements. Implicit systems arising from the semi-explicit time discretization of  the flow equations are solved with a p-multigrid preconditioned conjugate gradient method which minimizes the memory requirements and increase overall run time performance. Computations are localized mostly near the interface location to reduce computational cost without sacrificing the accuracy. The proposed method allows to capture interface topology accurately  in simulating wide range of flow regimes with high density/viscosity ratios and offers good mass conservation even in relatively coarse grids while keeping the simplicity of the level set interface modeling. Efficiency, local high-order accuracy and mass conservation of the method are confirmed through distinct numerical test cases of sloshing, dam break and Rayleigh-Taylor instability.

A GPU ACCELERATED LEVEL SET REINITIALIZATION FOR AN ADAPTIVE DISCONTINUOUS GALERKIN METHOD

August, 2016

Authors: Ali Karakus, Tim Warburton,  Haluk Aksel and Cuneyt Sert

​Computers & Mathematics with Applications

Abstract:GPU accelerated high order reconstruction of signed distance function of the level set method is studied. The flow based reinitialization equation is discretized in space by using a nodal discontinuous Galerkin method on adaptive unstructured grids. Artificial diffusion with a modal decay rate based regularity estimator is used to damp out high frequency solution components near kinks, where mesh adaptivity is applied. A two rate Adams-Bashforth time integrator is developed to avoid time step restrictions resulting from artificial diffusion stabilization and local mesh refinement. Platform independence of the solver is achieved by using an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable numerical scheme that preserves the simplicity of the original level set method is obtained. Performance and accuracy of the method to construct signed distance function on highly disturbed initial data with smooth and non-smooth interfaces are tested through distinct two- and three-dimensional problems.

A GPU-ACCELERATED ADAPTIVE DISCONTINUOUS GALERKIN METHOD FOR LEVEL SET EQUATION

March, 2016

Authors: Ali Karakus, Tim Warburton,  Haluk Aksel and Cuneyt Sert

International Journal of Computational Fluid Dynamics

Abstract:

This paper presents a GPU-accelerated nodal discontinuous Galerkin method for the solution of two- and three-dimensional level set (LS) equation on unstructured adaptive meshes. Using adaptive mesh refinement, computations are localised mostly near the interface location to reduce the computational cost. Small global time step size resulting from the local adaptivity is avoided by local time-stepping based on a multi-rate Adams–Bashforth scheme. Platform independence of the solver is achieved with an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable, accurate and mass conservative numerical scheme that preserves the simplicity of LS formulation is obtained. Efficiency, performance and local high-order accuracy of the method are demonstrated through distinct numerical test cases.