A Cartesian grid embedded boundary method for hyperbolic conservation laws

• Published in: Journal of computational physics Vol. 211; no. 1; pp. 347 - 366
• Main Authors: Colella, Phillip, Graves, Daniel T., Keen, Benjamin J., Modiano, David
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 2006; Elsevier
• Subjects: Boundaries; Cartesian; Computational techniques; Conservation laws; Discontinuity; Discretization; Exact sciences and technology; Hyperbolic systems; Mathematical methods in physics; Physics; Preserves; Stability; Conservation laws; Discontinuity; Second order; Hyperbolic system; Algorithms; Discretization; Mass difference; Calculation; Calculation methods
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2005.05.026

We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L 1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.