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A comparison of flux limited difference methods and characteristic Galerkin methods for shock modelling. (English) Zbl 0632.76077
A comparison is made between flux-limited finite difference methods and characteristic Galerkin methods for approximating hyperbolic conservation laws. At the first-order level, the characteristic Galerkin scheme using piecewise constants is closely related to the difference schemes of Engquist, Osher, and Roe [e.g.: B. Engquist and S. Osher, Math. Comput. 34, 45-75 (1980; Zbl 0438.76051)]. Adaptive recovery techniques used to improve accuracy then have much in common with the flux limiters used with difference methods. These relationships are explored and comarisons made using the linear advection, inviscid Burger equation and Euler equations. A new, simple formulation is given of the characteristic Galerkin method using piecewise constant elements with piecewise linear recovery: it reduces to the Engquist-Osher algorithm but with a modified flux function when the CFL number is no greater than one half.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics
Citations:
Zbl 0438.76051
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