Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces
A novel numerical scheme is proposed to solve the shallow water equations (SWEs) on arbitrary rotating curved surfaces. Based on the method of moving frames (MMF) in which the geometry is represented by orthonormal vectors, the proposed scheme not only has the fewest dimensionality both in space and...
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| Veröffentlicht in: | Journal of computational physics 2017-03, Vol.333, p.1-23 |
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| container_title | Journal of computational physics |
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| creator | Chun, S. Eskilsson, C. |
| description | A novel numerical scheme is proposed to solve the shallow water equations (SWEs) on arbitrary rotating curved surfaces. Based on the method of moving frames (MMF) in which the geometry is represented by orthonormal vectors, the proposed scheme not only has the fewest dimensionality both in space and time, but also does not require either of metric tensors, composite meshes, or the ambient space. The MMF–SWE formulation is numerically discretized using the discontinuous Galerkin method of arbitrary polynomial order p in space and an explicit Runge–Kutta scheme in time. The numerical model is validated against six standard tests on the sphere and the optimal order of convergence of p+1 is numerically demonstrated. The MMF–SWE scheme is also demonstrated for its efficiency and stability on the general rotating surfaces such as ellipsoid, irregular, and non-convex surfaces. |
| doi_str_mv | 10.1016/j.jcp.2016.12.013 |
| format | Article |
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Based on the method of moving frames (MMF) in which the geometry is represented by orthonormal vectors, the proposed scheme not only has the fewest dimensionality both in space and time, but also does not require either of metric tensors, composite meshes, or the ambient space. The MMF–SWE formulation is numerically discretized using the discontinuous Galerkin method of arbitrary polynomial order p in space and an explicit Runge–Kutta scheme in time. The numerical model is validated against six standard tests on the sphere and the optimal order of convergence of p+1 is numerically demonstrated. The MMF–SWE scheme is also demonstrated for its efficiency and stability on the general rotating surfaces such as ellipsoid, irregular, and non-convex surfaces.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2016.12.013</identifier><language>eng</language><publisher>Cambridge: Elsevier Inc</publisher><subject>Computational physics ; Curved surface ; Discontinuous Galerkin method ; Finite element analysis ; Frames ; Galerkin method ; High-order finite elements ; Mathematical analysis ; Mathematical functions ; Mathematical models ; Moving frames ; Numerical analysis ; Polynomials ; Rotation ; Runge-Kutta method ; Shallow water equations ; Spherical geometry ; Surface stability ; Tensors</subject><ispartof>Journal of computational physics, 2017-03, Vol.333, p.1-23</ispartof><rights>2016 Elsevier Inc.</rights><rights>Copyright Elsevier Science Ltd. 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The MMF–SWE scheme is also demonstrated for its efficiency and stability on the general rotating surfaces such as ellipsoid, irregular, and non-convex surfaces.</description><subject>Computational physics</subject><subject>Curved surface</subject><subject>Discontinuous Galerkin method</subject><subject>Finite element analysis</subject><subject>Frames</subject><subject>Galerkin method</subject><subject>High-order finite elements</subject><subject>Mathematical analysis</subject><subject>Mathematical functions</subject><subject>Mathematical models</subject><subject>Moving frames</subject><subject>Numerical analysis</subject><subject>Polynomials</subject><subject>Rotation</subject><subject>Runge-Kutta method</subject><subject>Shallow water equations</subject><subject>Spherical geometry</subject><subject>Surface stability</subject><subject>Tensors</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kEFv2zAMhYWiA5pm_QG7CdjZHik7ioSdhmDdBqToZTsLskQ3NhIrkeQE_fdTkJ13IQniPfLhY-wTQo2A8stYj-5YizLWKGrA5o4tEDRUYo3yni0ABFZaa3xgjymNAKBWrVqw7oXyLngeen4I52F64320B0o8B57C_kw874innd3vw4VfbKbI6TTbPIQp8TBxG7shRxvfeQy5rMsFN8czeZ7m2FtH6SP70Nt9oqd_fcn-PH__vflZbV9__Np821auEatcNUr2Dmml1rLrVAet8lorpaFtSm1l16PU3lrshPcOpFASwTW-VVq2aqWbJft8u3uM4TRTymYMc5zKSyNAol7rNUJR4U3lYkgpUm-OcTiU_AbBXFGa0RSU5orSoDAFZfF8vXmoxD8PFE1yA02O_BDJZePD8B_3XxFYfCw</recordid><startdate>20170315</startdate><enddate>20170315</enddate><creator>Chun, S.</creator><creator>Eskilsson, C.</creator><general>Elsevier Inc</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-0184-0090</orcidid></search><sort><creationdate>20170315</creationdate><title>Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces</title><author>Chun, S. ; Eskilsson, C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-386fc1e5876bb8b048d9988904388946bf169daa1b2ddc0628610c3d489648593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Computational physics</topic><topic>Curved surface</topic><topic>Discontinuous Galerkin method</topic><topic>Finite element analysis</topic><topic>Frames</topic><topic>Galerkin method</topic><topic>High-order finite elements</topic><topic>Mathematical analysis</topic><topic>Mathematical functions</topic><topic>Mathematical models</topic><topic>Moving frames</topic><topic>Numerical analysis</topic><topic>Polynomials</topic><topic>Rotation</topic><topic>Runge-Kutta method</topic><topic>Shallow water equations</topic><topic>Spherical geometry</topic><topic>Surface stability</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chun, S.</creatorcontrib><creatorcontrib>Eskilsson, C.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chun, S.</au><au>Eskilsson, C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces</atitle><jtitle>Journal of computational physics</jtitle><date>2017-03-15</date><risdate>2017</risdate><volume>333</volume><spage>1</spage><epage>23</epage><pages>1-23</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>A novel numerical scheme is proposed to solve the shallow water equations (SWEs) on arbitrary rotating curved surfaces. 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| ispartof | Journal of computational physics, 2017-03, Vol.333, p.1-23 |
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| language | eng |
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| subjects | Computational physics Curved surface Discontinuous Galerkin method Finite element analysis Frames Galerkin method High-order finite elements Mathematical analysis Mathematical functions Mathematical models Moving frames Numerical analysis Polynomials Rotation Runge-Kutta method Shallow water equations Spherical geometry Surface stability Tensors |
| title | Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces |
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