Abstract
We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge-averaged quantities, which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [1]. However, [1] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [1]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.
Highlights
In this paper, we present a conservative scheme based on the Spectral Deferred Corrections (SDC) and Piecewise Parabolic Method (PPM) methods
We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method
We present a conservative scheme based on the SDC and PPM methods
Summary
We present a conservative scheme based on the SDC and PPM methods. The integration of the SDC method to the PPM method was first carried out by Anita et al in [1]. The main reason for this behavior (as mentioned above) is that the higher order flux evaluation at the prediction step lacks of necessary numerical diffusion so as the correction steps leading to unwanted oscillations around discontinuities. We fix this behavior with the following strategy. We let the correction iterations include the higher order PPM fluxing With this strategy, we found out that solutions from the prediction step have enough numerical diffusion so that potential oscillations that might come from the correction steps are killed off.
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