ISI TAŞINIMI İÇİN YAPISAL OLMAYAN AĞLARDA BİR HIZLANDIRILMIŞ SÜREKSİZ GALERKİN METDU: FORMÜLASYONU VE DOĞRULANMASI

Abstract

Bu çalışmada, büyük ölçekli, birleştirilmiş sıkıştırılamaz akış ve ısı transferi problemleri için GPU ile hızlandırılmış bir yöntem sunulmuştur. Yapılandırılmamış üçgen ağlar üzerinde tanımlayıcı denklemlerini ayrıklaştırmak için yüksek dereceli, nodal süreksiz Galerkin yöntemi kullanılmıştır. Zaman ayrıklaştırması, taşınım terimlerinin açık bir şekilde ele alındığı, Stokes operatörlerinin ise örtük olarak çözüldüğü bir yarı-örtük şema kullanılarak elde edilmiştir. Basınç sistemi, tamamen GPU ile hızlandırılmış bir çoklu-ağ ön koşullandırıcının kullanıldığı, eşlenik gradyan yöntemiyle çözülmüştür. Kod, yüksek dereceli ayrıklaştırmalar için yüksek performanslı kerneller sağlayan, ölçeklenebilir kütüphane olan libParanumal üzerine yazılmıştır. Platformdan bağımsız performans taşınabilirliği OCCA (open concurrent compute abstraction) dili ile elde edilmiştir. Yapılan serbest ve karışık taşınım problemlerini içeren bir dizi sayısal test ile sunulan metodun deneysel olarak beklenen, spektral doğruluğa ulaştığını gösterilmiştir.

Keywords

• süreksiz Galerkin
• GPU
• paralel
• sıkıştırılamaz akış
• ısı transferi
• yüksek seviyeli hesaplama.

AN ACCELERATED NODAL DISCONTINUOUS GALERKIN METHOD FOR THERMAL CONVECTION ON UNSTRUCTURED MESHES: FORMULATION AND VALIDATION

Abstract

We present a GPU-accelerated method for large scale, coupled incompressible fluid flow and heat transfer problems. A high-order, nodal discontinuous Galerkin method is utilized to discretize governing equations on unstructured triangular meshes. A semi-implicit scheme with explicit treatment of the advective terms and implicit treatment of the split Stokes operators are used for time discretization. The pressure system is solved with a conjugate gradient method together with a fully GPU-accelerated multigrid preconditioner. The code is built on scalable libParanumal solver which is a library of high-performance kernels for high-order discretizations. Performance portability is achieved by using the open concurrent compute abstraction, OCCA. A set of numerical experiments including free and mixed convection problems indicate that our approach experimentally reaches design order of accuracy.

Keywords

• discontinuous Galerkin
• GPU
• parallel
• incompressible
• heat transfer
• high-order.

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