High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

McCorquodale, P. W.; Colella, P.; Dorr, M. R.; Hittinger, J. A. F.

doi:10.1016/j.jcp.2015.01.006

Title: High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

Journal Article · Tue Jan 13 00:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.01.006· OSTI ID:1249128

McCorquodale, P. W. ^[1]; Colella, P. ^[1]; Dorr, M. R. ^[2]; Hittinger, J. A. F. ^[2]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

We present an approach to solving hyperbolic conservation laws by finite-volume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) [10] for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. We demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC52-07NA27344; AC02-05CH11231

OSTI ID:: 1249128

Alternate ID(s):: OSTI ID: 1236619; OSTI ID: 1247035; OSTI ID: 1407349

Report Number(s):: LLNL-JRNL-652819; LBNL-182615

Journal Information:: Journal of Computational Physics, Vol. 288, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 16 works

Citation information provided by
Web of Science

References (25)

Stability of interfaces with mesh refinement Berger, Marsha J. Mathematics of Computation, Vol. 45, Issue 172 https://doi.org/10.1090/S0025-5718-1985-0804925-4	journal	January 1985
On Conservation at Grid Interfaces Berger, Marsha J. SIAM Journal on Numerical Analysis, Vol. 24, Issue 5 https://doi.org/10.1137/0724063	journal	October 1987
Adaptive zoning for singular problems in two dimensions Brackbill, J. U.; Saltzman, J. S. Journal of Computational Physics, Vol. 46, Issue 3 https://doi.org/10.1016/0021-9991(82)90020-1	journal	June 1982
A Scheme for Conservative Interpolation on Overlapping Grids Chesshire, G.; Henshaw, W. D. SIAM Journal on Scientific Computing, Vol. 15, Issue 4 https://doi.org/10.1137/0915051	journal	July 1994
High-order, finite-volume methods in mapped coordinates Colella, P.; Dorr, M. R.; Hittinger, J. A. F. Journal of Computational Physics, Vol. 230, Issue 8 https://doi.org/10.1016/j.jcp.2010.12.044	journal	April 2011
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows Ivan, Lucian; Groth, Clinton P. T. Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.09.045	journal	January 2014
Multi-dimensional finite-volume scheme for hyperbolic conservation laws on three-dimensional solution-adaptive cubed-sphere grids Ivan, Lucian; De Sterck, Hans; Northrup, Scott A. Journal of Computational Physics, Vol. 255 https://doi.org/10.1016/j.jcp.2013.08.008	journal	December 2013
Euler Solution Using Cartesian Grid with a Gridless Least-Squares Boundary Treatment Koh, E. P. C.; Tsai, H. M.; Liu, F. AIAA Journal, Vol. 43, Issue 2 https://doi.org/10.2514/1.6177	journal	February 2005
Numerical treatment of two-dimensional interfaces for acoustic and elastic waves Lombard, Bruno; Piraux, Joël Journal of Computational Physics, Vol. 195, Issue 1 https://doi.org/10.1016/j.jcp.2003.09.024	journal	March 2004
Inviscid transonic flow over airfoils Magnus, R.; Yoshihara, H. AIAA Journal, Vol. 8, Issue 12 https://doi.org/10.2514/3.6080	journal	December 1970
High resolution finite volume computations on unstructured grids using solution dependent weighted least squares gradients Mandal, J. C.; Rao, Sundeep P. Computers & Fluids, Vol. 44, Issue 1 https://doi.org/10.1016/j.compfluid.2010.11.021	journal	May 2011
A high-order finite-volume method for conservation laws on locally refined grids McCorquodale, Peter; Colella, Phillip Communications in Applied Mathematics and Computational Science, Vol. 6, Issue 1 https://doi.org/10.2140/camcos.2011.6.1	journal	January 2011
A high-order accurate unstructured finite volume Newton–Krylov algorithm for inviscid compressible flows Nejat, Amir; Ollivier-Gooch, Carl Journal of Computational Physics, Vol. 227, Issue 4 https://doi.org/10.1016/j.jcp.2007.11.011	journal	February 2008
Stability of interpolation on overlapping grids Olsson, Fredrik; Petersson, N. Anders Computers & Fluids, Vol. 25, Issue 6 https://doi.org/10.1016/0045-7930(96)00020-5	journal	July 1996
Conservative and non-conservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems Pärt-Enander, Eva; Sjögreen, Björn Computers & Fluids, Vol. 23, Issue 3 https://doi.org/10.1016/0045-7930(94)90019-1	journal	March 1994
A conservative treatment of zonal boundaries for euler equation calculations Mohan Rai, Man Journal of Computational Physics, Vol. 62, Issue 2 https://doi.org/10.1016/0021-9991(86)90141-5	journal	February 1986
The “Cubed Sphere”: A New Method for the Solution of Partial Differential Equations in Spherical Geometry Ronchi, C.; Iacono, R.; Paolucci, P. S. Journal of Computational Physics, Vol. 124, Issue 1 https://doi.org/10.1006/jcph.1996.0047	journal	March 1996
High-order compact finite-difference methods on general overset grids Sherer, Scott E.; Scott, James N. Journal of Computational Physics, Vol. 210, Issue 2 https://doi.org/10.1016/j.jcp.2005.04.017	journal	December 2005
Fusion Plasma Physics Stacey, Weston M. Wiley‐VCH Verlag GmbH & Co. https://doi.org/10.1002/9783527669516	book	August 2012
Composite mesh difference methods for elliptic boundary value problems Starius, G�ran Numerische Mathematik, Vol. 28, Issue 2 https://doi.org/10.1007/BF01394455	journal	June 1977
On the use of composite grid schemes in computational aerodynamics Steger, Joseph L.; Benek, John A. Computer Methods in Applied Mechanics and Engineering, Vol. 64, Issue 1-3 https://doi.org/10.1016/0045-7825(87)90045-4	journal	October 1987
High-order central ENO finite-volume scheme for ideal MHD Susanto, A.; Ivan, L.; De Sterck, H. Journal of Computational Physics, Vol. 250 https://doi.org/10.1016/j.jcp.2013.04.040	journal	October 2013
Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review Thompson, Joe F.; Warsi, Zahir U. A.; Wayne Mastin, C. Journal of Computational Physics, Vol. 47, Issue 1 https://doi.org/10.1016/0021-9991(82)90066-3	journal	July 1982
High-order finite-volume methods for the shallow-water equations on the sphere Ullrich, Paul A.; Jablonowski, Christiane; van Leer, Bram Journal of Computational Physics, Vol. 229, Issue 17 https://doi.org/10.1016/j.jcp.2010.04.044	journal	August 2010
An analysis of finite-difference and finite-volume formulations of conservation laws Vinokur, Marcel Journal of Computational Physics, Vol. 81, Issue 1 https://doi.org/10.1016/0021-9991(89)90063-6	journal	March 1989

Cited By (6)

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R. Journal of Scientific Computing, Vol. 77, Issue 2 https://doi.org/10.1007/s10915-018-0726-6	journal	May 2018
High-Order Finite-Volume Method with Block-Based AMR for Magnetohydrodynamics Flows Freret, L.; Ivan, L.; De Sterck, H. Journal of Scientific Computing, Vol. 79, Issue 1 https://doi.org/10.1007/s10915-018-0844-1	journal	October 2018
Continuum kinetic modeling of the tokamak plasma edge Dorf, M. A.; Dorr, M. R.; Hittinger, J. A. Physics of Plasmas, Vol. 23, Issue 5 https://doi.org/10.1063/1.4943106	journal	May 2016
Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R. arXiv https://doi.org/10.48550/arxiv.1707.08247	preprint	January 2017
Implicit gas-kinetic unified algorithm based on multi-block docking grid for multi-body reentry flows covering all flow regimes Peng, Ao-Ping; Li, Zhi-Hui; Wu, Jun-Lin Journal of Computational Physics, Vol. 327 https://doi.org/10.1016/j.jcp.2016.09.050	journal	December 2016
Magnetic Fluctuations in Gyrokinetic Simulations of Tokamak Scrape-Off Layer Turbulence Mandell, Noah arXiv https://doi.org/10.48550/arxiv.2103.16062	preprint	January 2021

Similar Records

A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids

Journal Article · Fri Jan 28 00:00:00 EST 2011 · Communications in Applied Mathematics and Computational Science · OSTI ID:1249128

McCorquodale, Peter; Colella, Phillip

Triangle based TVD schemes for hyperbolic conservation laws. Final report

Technical Report · Mon Jan 01 00:00:00 EST 1990 · OSTI ID:1249128

Durlofsky, L J; Osher, S; Engquist, B

High-order Finite-volume Methods for Hyperbolic Conservation Laws on Mapped Multiblock Grids

Journal Article · Mon Jan 26 00:00:00 EST 2015 · Journal of Computational Physics · OSTI ID:1249128

McCorquodale, P; Dorr, M R; Hittinger, J F; +1 more

Related Subjects

97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
finite-volume method
high-order discretization
mapped grids
multiblock
hyperbolic partial differential equations

Title: High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

Citation Formats

References (25)

Cited By (6)

Similar Records

Related Subjects