GPU accelerated high-order discontinuous galerkin level set methods for incompressible multiphase flows

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Makina Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2015

Öğrenci: ALİ KARAKUŞ

Eş Danışman: CÜNEYT SERT, MEHMET HALUK AKSEL

Özet:

This thesis study focuses on the development of GPU accelerated, high-order discontinuous Galerkin methods for the solution of unsteady incompressible and immiscible multiphase flows with level set interface representation. Nodal discontinuous Galerkin framework is used for Navier-Stokes, level set evolution and reinitialization equations on unstructured elements. Computations are localized mostly near the interface location with an adaptive method to reduce computational cost without sacrificing the accuracy. An artificial diffusion approach with a modal decay rate based regularity estimator is used to damp out high frequency solution components near kinks. For the computation of interface equations, a multi-rate Adams-Bashforth time integrator is designed to avoid time step restrictions resulting from artificial diffusion stabilization and local mesh refinement. Implicit systems arising from the semi-explicit time discretization of the flow equations are solved with a matrix-free $ p $-multigrid preconditioned conjugate gradient method to minimize memory requirements and to increase overall runtime performance. The developed numerical scheme is accelerated using modern GPUs and many-core CPUs. Platform independence of the solver is achieved with an extensible multi-threading programming API as common kernel language that allows runtime selection of different computing devices and threading interfaces. Efficiency, scalability, local high-order accuracy and mass conservation of the method are confirmed through distinct numerical test cases.