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

Abstract

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.

Authors:
 [1];  [1];  [2];  [2]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1249128
Alternate Identifier(s):
OSTI ID: 1236619; OSTI ID: 1247035; OSTI ID: 1407349
Report Number(s):
LLNL-JRNL-652819; LBNL-182615
Journal ID: ISSN 0021-9991
Grant/Contract Number:  
AC52-07NA27344; AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 288; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; finite-volume method; high-order discretization; mapped grids; multiblock; hyperbolic partial differential equations

Citation Formats

McCorquodale, P. W., Colella, P., Dorr, M. R., and Hittinger, J. A. F. High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2015.01.006.
McCorquodale, P. W., Colella, P., Dorr, M. R., & Hittinger, J. A. F. High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids. United States. https://doi.org/10.1016/j.jcp.2015.01.006
McCorquodale, P. W., Colella, P., Dorr, M. R., and Hittinger, J. A. F. 2015. "High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids". United States. https://doi.org/10.1016/j.jcp.2015.01.006. https://www.osti.gov/servlets/purl/1249128.
@article{osti_1249128,
title = {High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids},
author = {McCorquodale, P. W. and Colella, P. and Dorr, M. R. and Hittinger, J. A. F.},
abstractNote = {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.},
doi = {10.1016/j.jcp.2015.01.006},
url = {https://www.osti.gov/biblio/1249128}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = C,
volume = 288,
place = {United States},
year = {Tue Jan 13 00:00:00 EST 2015},
month = {Tue Jan 13 00:00:00 EST 2015}
}

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Cited by: 16 works
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Works referenced in this record:

Stability of interfaces with mesh refinement
journal, January 1985


On Conservation at Grid Interfaces
journal, October 1987


Adaptive zoning for singular problems in two dimensions
journal, June 1982


A Scheme for Conservative Interpolation on Overlapping Grids
journal, July 1994


High-order, finite-volume methods in mapped coordinates
journal, April 2011


High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
journal, January 2014


Multi-dimensional finite-volume scheme for hyperbolic conservation laws on three-dimensional solution-adaptive cubed-sphere grids
journal, December 2013


Euler Solution Using Cartesian Grid with a Gridless Least-Squares Boundary Treatment
journal, February 2005


Numerical treatment of two-dimensional interfaces for acoustic and elastic waves
journal, March 2004


Inviscid transonic flow over airfoils
journal, December 1970


A high-order finite-volume method for conservation laws on locally refined grids
journal, January 2011


A high-order accurate unstructured finite volume Newton–Krylov algorithm for inviscid compressible flows
journal, February 2008


Stability of interpolation on overlapping grids
journal, July 1996


A conservative treatment of zonal boundaries for euler equation calculations
journal, February 1986


The “Cubed Sphere”: A New Method for the Solution of Partial Differential Equations in Spherical Geometry
journal, March 1996


High-order compact finite-difference methods on general overset grids
journal, December 2005


Fusion Plasma Physics
book, August 2012


Composite mesh difference methods for elliptic boundary value problems
journal, June 1977


On the use of composite grid schemes in computational aerodynamics
journal, October 1987


High-order central ENO finite-volume scheme for ideal MHD
journal, October 2013


Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review
journal, July 1982


High-order finite-volume methods for the shallow-water equations on the sphere
journal, August 2010


An analysis of finite-difference and finite-volume formulations of conservation laws
journal, March 1989


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Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration
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High-Order Finite-Volume Method with Block-Based AMR for Magnetohydrodynamics Flows
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Continuum kinetic modeling of the tokamak plasma edge
journal, May 2016