Shape-preserving finite elements in cylindrical and spherical geometries: The double Jacobian approach

Morgan，Jason P.1,2,4; Taramón，Jorge M.2; Hasenclever，Jörg3

2020

10.1002/fld.4799

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS   影响因子和分区

0271-2091

1097-0363

We present a new technique, the “double Jacobian,” to solve problems in cylindrical or spherical geometries, for example, the Stokes flow problem for convection in Earth's mantle. Our approach combines the advantages of working simultaneously in Cartesian and polar or spherical coordinates. The governing matrix equations are kept in Cartesian coordinates, thereby preserving their Cartesian symmetry. However, the element geometry is described as a linear simplex in polar or spherical coordinates, thereby preserving appropriate cylindrical or spherical surfaces and internal interfaces. Isoparametric representations can still be used to define complex surface shapes. Using linear polar or spherical elements allows search routines for triangular or tetrahedral simplexes to rapidly find arbitrary points in terms of their polar or spherical coordinates. The double Jacobian approach becomes especially powerful when element sizes vary strongly within the mesh, while the exact cylindrical or spherical surfaces or internal interfaces have to be preserved, as happens in several geophysical applications.

convection double Jacobian approach finite element free surface integration natural convection stability

SCI ; EI

英语

第一 ; 通讯

WOS:000514280000001

20200908211295

Finite element method ; Matrix algebra ; Natural convection

Heat Transfer:641.2 ; Algebra:921.1 ; Numerical Methods:921.6

ENGINEERING

2-s2.0-85079887643

Scopus

1.Department of Ocean Science and Engineering,SUSTech,Shenzen,China
2.Department of Earth Sciences,Royal Holloway University of London,Egham,United Kingdom
3.Institute of Geophysics,Hamburg University,Hamburg,Germany
4.Jason P. Morgan,Department of Ocean Science and Engineering,SUSTech,Shenzhen,China

Morgan，Jason P.,Taramón，Jorge M.,Hasenclever，Jörg. Shape-preserving finite elements in cylindrical and spherical geometries: The double Jacobian approach[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS,2020,92:635-668.

Morgan，Jason P.,Taramón，Jorge M.,&Hasenclever，Jörg.(2020).Shape-preserving finite elements in cylindrical and spherical geometries: The double Jacobian approach.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS,92,635-668.

Morgan，Jason P.,et al."Shape-preserving finite elements in cylindrical and spherical geometries: The double Jacobian approach".INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 92(2020):635-668.