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A higher-order boundary treatment for Cartesian-grid methods. (English) Zbl 0936.76041
Summary: The Euler equations describe the flow phenomena of compressible inviscid gas dynamics. The authors simulate such flows using a higher-order Cartesian-grid method, together with a special treatment for the cells cut by the boundary of an object. A new method for the treatment of the boundary is described where these cut boundary cells are maintained as whole cells rather than as cut cells, thus avoiding stability problems. The method is second-order accurate in one dimension and higher-order accurate in two dimensions, but not strictly conservative. However, they show that this error in the conservation does not lead to spurious phenomena on some representative test calculations. The advantages of the new boundary treatment are that it is higher-order accurate, that it is independent of the applied method and that it is simple.

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
Full Text: DOI
[1] Berger, M. J.; LeVeque, R. J., A Rotated Difference Scheme for Cartesian Grids in Complex Geometries, (1991)
[2] Coirier, W. J.; Powell, K. G., An accuracy assessment of Cartesian-mesh approaches for the Euler equations, J. Comput. Phys., 117, 121, (1995) · Zbl 0817.76055
[3] Dervieux, A.; van Leer, B., GAMM workshop on Numerical Solution of the Euler Equation, 26, (1989)
[4] Forrer, H., Boundary Treatment for a Cartesian Grid Method, (1996)
[5] R. J. LeVeque,
[6] LeVeque, R. J., Numerical Methods for Conservation Laws, (1992) · Zbl 0847.65053
[7] LeVeque, R. J., Simplified multi-dimensional flux limiter methods, Numer. Methods Fluid Dyn., 4, 175, (1993) · Zbl 0801.76069
[8] Jeltsch, R.; Botta, N., A numerical method for unsteady flows, Appl. Math., 40, 175, (1995) · Zbl 0831.76064
[9] Pember, R. B.; Bell, J. B.; Colella, P.; Crutchfield, W. Y.; Welcome, M. L., An adaptive Cartesian grid method for unsteady compressible flow in irregular regions, J. Comput. Phys., 120, 278, (1995) · Zbl 0842.76056
[10] Quirk, J. J., An alternative to unstructered grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies, Comput. Fluids, 23, 125, (1994) · Zbl 0788.76067
[11] Roe, P. L., Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43, 357, (1981) · Zbl 0474.65066
[12] Thomas, J. L.; Salas, M. D., Far-field boundary conditions for transonic lifting solutions to the Euler equations, AIAA Journal, 24, (1986)
[13] Wendroff, B.; White, A., On Irregular Grids, 24, (1988)
[14] Woodward, P.; Colella, P., The numerical simulation of 2D fluid flow with strong shocks, J. Comp. Phys., 54, 115, (1984) · Zbl 0573.76057
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