THE PIECEWISE-PARABOLIC METHOD (PPM) FOR GAS-DYNAMICAL SIMULATIONS

THE PIECEWISE-PARABOLIC METHOD (PPM) FOR GAS-DYNAMICAL SIMULATIONS

July 1982 | Phillip Colella, Paul R. Woodward
The paper presents the Piecewise-Parabolic Method (PPM), a higher-order extension of Godunov's method for gas dynamics simulations. The PPM method introduces several new features, including a higher-order spatial interpolation that allows for steeper representation of discontinuities, particularly contact discontinuities. It also includes a simpler and more robust algorithm for calculating nonlinear wave interactions used to compute fluxes, and additional dissipation to improve accuracy. The method is described in detail for both Lagrangian and Eulerian coordinates, with specific algorithms for handling discontinuities and dissipation mechanisms. The authors discuss the advantages and limitations of the PPM method, emphasizing its ability to produce sharp discontinuities and accurate solutions even in the presence of strong shocks. The paper concludes with a discussion of the types of dissipation required in these schemes and the results of test calculations involving strong shocks.The paper presents the Piecewise-Parabolic Method (PPM), a higher-order extension of Godunov's method for gas dynamics simulations. The PPM method introduces several new features, including a higher-order spatial interpolation that allows for steeper representation of discontinuities, particularly contact discontinuities. It also includes a simpler and more robust algorithm for calculating nonlinear wave interactions used to compute fluxes, and additional dissipation to improve accuracy. The method is described in detail for both Lagrangian and Eulerian coordinates, with specific algorithms for handling discontinuities and dissipation mechanisms. The authors discuss the advantages and limitations of the PPM method, emphasizing its ability to produce sharp discontinuities and accurate solutions even in the presence of strong shocks. The paper concludes with a discussion of the types of dissipation required in these schemes and the results of test calculations involving strong shocks.
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