We discuss how to combine a front tracking method with dimensional splitting to solve systems of conservation laws numerically in two space dimensions. In addition we present an adaptive grid refinement strategy. The method is unconditionally stable and allows for moderately high CFL numbers (typica
An improved front tracking method for the Euler equations
β Scribed by J.A.S. Witteveen; B. Koren; P.G. Bakker
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 369 KB
- Volume
- 224
- Category
- Article
- ISSN
- 0021-9991
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β¦ Synopsis
An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as compared to standard front tracking methods. The resulting algorithm is also more efficient than existing front tracking methods. The improved front tracking method is applied to the Euler equations for one-dimensional unsteady flow and two-dimensional steady supersonic flow. The results are compared to results of a standard front tracking method and a finite volume method.
π SIMILAR VOLUMES
An adaptive least-squares finite element method is used to solve the compressible Euler equations in two dimensions. Since the method is naturally diffusive, no explicit artificial viscosity is added to the formulation. The inherent artificial viscosity, however, is usually large and hence does not
## Communicated by D. G. Crighton Abstract--We prove that for an ideal incompressible fluid in the presence of a conservative body force, there exists a time invariant, a vector A ---(Jtl,.42,.A3). It is discussed that the invariance of Ai is probably linked to geometrical structures of Navier-Sto