Nonlinear filters for efficient shock computation

Authors:
Björn Engquist, Per Lötstedt and Björn Sjögreen

Journal:
Math. Comp. **52** (1989), 509-537

MSC:
Primary 65M05; Secondary 35L65

DOI:
https://doi.org/10.1090/S0025-5718-1989-0955750-9

MathSciNet review:
955750

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Abstract: A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0955750-9

Article copyright:
© Copyright 1989
American Mathematical Society