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Time dependent boundary conditions for hyperbolic systems. (English) Zbl 0619.76089
Time dependent numerical models for hyperbolic systems, such as the fluid dynamics equations, require time dependent boundary conditions when the systems are solved in a finite domain. The ”correct” boundary condition depends on the external solution, but for many problems the external solution is not known. In such cases nonreflecting boundary conditions often produce solutions with the desired behavior. This paper extends the concept of non-reflecting boundary conditions to the multidimensional case in non-rectangular coordinate systems. Results are given for several fluid dynamics test problems: the traveling shock wave, shock tube, spherical explosion, and homologous expansion problems in one dimension, and a traveling shock wave moving at a 45\(\circ\) angle with respect to the x axis in two dimensions.

76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics
65N06 Finite difference methods for boundary value problems involving PDEs
35L05 Wave equation
80A25 Combustion
35L65 Hyperbolic conservation laws
Full Text: DOI
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