Abstract
The solutions of the compressible Euler equations are obtained as limit of the solutions of the Navier-Stokes equations when the viscosity and the heat conductivity tend to zero. First, the spatial derivatives in the NavierStokes equations are approximated by the least squares method and then the resulting system of ODEs is solved by an explicit second order Runge-Kutta method. The scheme is tested for the 1D shock tube problem. Also a fix grid Lagrangian method is proposed and the numerical results are compared with those from the moving grid approach.
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Tiwari, S. (2001). A LSQ-SPH Approach for Solving Compressible Viscous Flows. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_44
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DOI: https://doi.org/10.1007/978-3-0348-8372-6_44
Publisher Name: Birkhäuser, Basel
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