TY - GEN
T1 - AMixed explicit implicit time stepping scheme for cartesian embedded boundary meshes
AU - May, Sandra
AU - Berger, Marsha
N1 - Funding Information:
The authors would like to thank Ann Almgren, John Bell, and Andy Nonaka from Lawrence Berkeley National Laboratory for providing and helping the authors with the software packages BoxLib and VarDen. This work was supported in part by the DOE office of Advanced Scientific Computing under grant DE-FG02-88ER25053 and by AFOSR grant FA9550-13-1-0052. S. M. was also supported by ERC STG. N 306279, SPARCLE.
Publisher Copyright:
© Springer International Publishing Switzerland 2014.
PY - 2014
Y1 - 2014
N2 - We present a mixed explicit implicit time stepping scheme for solving the linear advection equationMay, Sandra on a Cartesian embedded boundary mesh. The scheme represents a new approach for overcoming the small cell problem—that standard finite volume schemes are not stable on the arbitrarily small cut cells. It uses implicit time stepping on cut cells for stability. On standard Cartesian cells, explicit time stepping is employed. This keeps the cost small and makes it possible to extend existing schemes from Cartesian meshes to Cartesian embedded boundary meshes. The coupling is done by flux bounding, for which we can prove a TVD result. We present numerical results in one and two dimensions showing secondorder convergence in the L1norm and between first- and second-order convergence in the L∞ norm.
AB - We present a mixed explicit implicit time stepping scheme for solving the linear advection equationMay, Sandra on a Cartesian embedded boundary mesh. The scheme represents a new approach for overcoming the small cell problem—that standard finite volume schemes are not stable on the arbitrarily small cut cells. It uses implicit time stepping on cut cells for stability. On standard Cartesian cells, explicit time stepping is employed. This keeps the cost small and makes it possible to extend existing schemes from Cartesian meshes to Cartesian embedded boundary meshes. The coupling is done by flux bounding, for which we can prove a TVD result. We present numerical results in one and two dimensions showing secondorder convergence in the L1norm and between first- and second-order convergence in the L∞ norm.
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U2 - 10.1007/978-3-319-05684-5_38
DO - 10.1007/978-3-319-05684-5_38
M3 - Conference contribution
AN - SCOPUS:84927656546
T3 - Springer Proceedings in Mathematics and Statistics
SP - 393
EP - 400
BT - Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7
A2 - Rohde, Christian
A2 - Fuhrmann, Jürgen
A2 - Ohlberger, Mario
PB - Springer New York LLC
T2 - 7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7
Y2 - 15 June 2014 through 20 June 2014
ER -