{"id":7972,"date":"2012-07-26T14:24:49","date_gmt":"2012-07-26T11:24:49","guid":{"rendered":"http:\/\/hgpu.org\/?p=7972"},"modified":"2012-07-26T14:24:49","modified_gmt":"2012-07-26T11:24:49","slug":"efficient-implementation-of-the-cpr-formulation-for-the-navier-stokes-equations-on-gpus","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=7972","title":{"rendered":"Efficient Implementation of the CPR Formulation for the Navier-Stokes Equations on GPUs"},"content":{"rendered":"<p>The correction procedure via reconstruction (CPR) formulation for the Euler and Navier-Stokes equations is implemented on a NVIDIA graphics processing unit (GPU) using CUDA C with both explicit and implicit time-stepping schemes for 2D unstructured triangular grids. For the implicit time integration, a first order time approximation with Newton iteration and Gauy elimination is used to solve the system of equations, while for explicit time-stepping a 3-stage Runge-Kutta scheme is used. For the implicit time-stepping on the GPU a preconditioned mesh coloring algorithm is developed, which is derived from the Four Color Theorem known from the graph theory. For the speed-up, compared to a single core of an Intel Xeon CPU, a factor up to 112-130 for explicit time-stepping is achieved, varying on the polynomial degree k and the chosen numerical flow. For the implicit time-stepping the maximum speed-up is between 47 and 89. All calculations are made in double precision using a single NVIDIA Tesla C2050.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The correction procedure via reconstruction (CPR) formulation for the Euler and Navier-Stokes equations is implemented on a NVIDIA graphics processing unit (GPU) using CUDA C with both explicit and implicit time-stepping schemes for 2D unstructured triangular grids. For the implicit time integration, a first order time approximation with Newton iteration and Gauy elimination is used [&hellip;]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[36,89,104,3],"tags":[1787,14,1795,158,122,120,20,378],"class_list":["post-7972","post","type-post","status-publish","format-standard","hentry","category-algorithms","category-nvidia-cuda","category-fluid-dynamics","category-paper","tag-algorithms","tag-cuda","tag-fluid-dynamics","tag-graph-theory","tag-navier-stokes-equations","tag-nses","tag-nvidia","tag-tesla-c2050"],"views":2454,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/7972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7972"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/7972\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}