A PIECEWISE-PARABOLIC METHOD USE FOR SOLVING ADVECTION EQUATION IN EGAK++ COMPLEX
P.A. Kucherova, Yu.V. Yanilkin, E.A. Goncharov
VANT. Ser.: Mat. Mod. Fiz. Proc 2003. Вып.1. С. 29-35.
The paper proposes the 2D piecewise-parabolic method (PPM method) with a new algorithm of solution monotonization to enhance the order of approximating convective members of gas-dynamic equations at the second computation stage in Lagrangian Eulerian method of EGAK++ complex. PPM method is used for calculating density and energy flows. After estimation of mass and energy flows they are corrected so as to monotonize the solution in the case of maximum principle violation, as the above algorithm does not provide this principle implementation. A new algorithm for solution monotinization has been proposed. The paper presents comparative properties of donor and piecewise-parabolic methods with monotonization algorithm based on 1 D and 2 D test and methodical problems. The piecewise-parabolic method with solution monotonization algorithm was developed and implemented in EGAK++ complex for computing problems on both regular and refined meshes. The distinctions in formulas, appearing under calculation on the refined mesh are studied. The results of computations with PPM method on regular and refined meshes are given.
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