In this thesis, well-balanced, central-upwind high-resolution methods of high order are developed for the two-dimensional shallow water equations, on the graphics processing unit (GPU). The methods are based on a fifth-order Weighted Essentially Non-Oscillating (WENO) reconstruction technique and a fourth-order Gaussian quadrature for the one-sided interface fluxes. Two schemes are implemented, one with bilinear interpolation of the bottom topography and a second-order quadrature for the bed slope source term, and one with a fourth-order source term quadrature and a fifth-order hydrostatic WENO reconstruction of the water height. The high-order schemes are compared to a second-order scheme by Kurganov and Petrova, which recently has been implemented on the GPU by Brodtkorb.The schemes are shown to be well-balanced and are capable of outperforming the second-order scheme on smooth problems provided that dry states and discontinuities do not occur. The performance gain is larger after a low number of time steps, where speed-ups by a factor between 3 and 8 are documented. As the system evolves, the accuracy of the high-order methods drops, and the performance gain is reduced to a factor around 1.5. The schemes do, however, not support outflow and inflow boundary conditions, and are not yet tested on real-world problems.The high-order scheme using the hydrostatic reconstruction and a fourth-order source term quadrature is implemented in such a way that an extension to quadratures and reconstructions of even higher order, should be fairly straight forward.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this thesis, well-balanced, central-upwind high-resolution methods of high order are developed for the two-dimensional shallow water equations, on the graphics processing unit (GPU). The methods are based on a fifth-order Weighted Essentially Non-Oscillating (WENO) reconstruction technique and a fourth-order Gaussian quadrature for the one-sided interface fluxes. Two schemes are implemented, one with bilinear interpolation […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","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":[11,89,157,3],"tags":[1782,14,1796,20,1183,390],"class_list":["post-9331","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-nvidia-cuda","category-mathematics","category-paper","tag-computer-science","tag-cuda","tag-mathematics","tag-nvidia","tag-nvidia-quadro-fx-5000","tag-thesis"],"views":2354,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/9331","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=9331"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/9331\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9331"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9331"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}