A kinetic method for strictly nonlinear conservation laws (Q1175299)
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scientific article; zbMATH DE number 11323
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A kinetic method for strictly nonlinear conservation laws |
scientific article; zbMATH DE number 11323 |
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A kinetic method for strictly nonlinear conservation laws (English)
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25 June 1992
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The authors propose a new solution method for nonlinear scalar conservation laws. The technique is based on increasing the dimension by introducing an artificial velocity-type variable \(\xi\) and choosing a suitable distribution function \(G(t,x,\xi)\) for which a linear kinetic equation holds. From \(G\) the solution to the original problem can be recovered by integration with respect to \(\xi\). Using a time step and various discretizations in space, a number of numerical methods are obtained. Among them are well-known upstream methods.
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weak solutions
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Cauchy problem
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non-smooth region
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upstream finite difference methods
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scalar conservation laws
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artificial velocity-type variable
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suitable distribution function
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linear kinetic equation
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time step
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discretizations in space
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