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Time-dependent boundary conditions for hyperbolic systems. II. (English) Zbl 0701.76070
Summary: Part I [the author, ibid. 68, 1-24 (1987; Zbl 0619.76089)] introduced the concept of nonreflecting boundary conditions for hyperbolic equations in more than one dimension. This paper develops a general boundary condition formalism for all types of boundary conditions to which hyperbolic systems are subject (including the nonreflecting conditions). The formalism is described in detail, and many examples are provided for common problems in hydrodynamics, including solid wall and nonreflecting boundaries.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
65N06 Finite difference methods for boundary value problems involving PDEs
35L05 Wave equation
80A25 Combustion
35L65 Hyperbolic conservation laws
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[1] Thompson, K.W., J. comput. phys., 68, 1, (1987)
[2] Thompson, K.W., Lecture series in computational fluid dynamics, ()
[3] Whitham, G.B., Linear and nonlinear waves, (1974), Wiley New York · Zbl 0373.76001
[4] Courant, R.; Friedrichs, K.O., Supersonic flow and shock waves, (1948), Springer-Verlag New York · Zbl 0041.11302
[5] Vanajakshi, T.C.; Thompson, K.W.; Black, D.C., J. comput. phys., 84, 343, (1989)
[6] Hedstrom, G.W., J. comput. phys., 30, 222, (1979)
[7] Landau, L.D.; Lifshitz, E.M., Fluid mechanics, (1959), Pergamon Elsmford, NY · Zbl 0146.22405
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