On meshless collocation approximations of conservation laws: Preliminary investigations on positive schemes and dissipation models (Q2731261)
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scientific article; zbMATH DE number 1625685
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On meshless collocation approximations of conservation laws: Preliminary investigations on positive schemes and dissipation models |
scientific article; zbMATH DE number 1625685 |
Statements
1 November 2001
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positive schemes
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dissipation models
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numerical examples
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meshless collocation methods
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transport processes
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hyperbolic conservation laws
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gas dynamics
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Lax-Friedrichs scheme
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shocks
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On meshless collocation approximations of conservation laws: Preliminary investigations on positive schemes and dissipation models (English)
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Meshless collocation methods for the numerical solution of transport processes described by hyperbolic conservation laws are considered. The future goal is the construction of a robust and reliable meshfree discretization method for the equations of gas dynamics in complex geometries. First, the simplest scalar model problems and analyze basic problems occuring in the grid-free approach is sudied. A topological condition on clouds of points is derived and several possible versions of a generalized Lax-Friedrichs scheme are discussed with respect to their numerical dissipation. A moving least-squares approach is followed to construct a possitive discretization for solutions with shocks which is thoroughly analyzed and applied to test problems.
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