An Explicit High-Order Single-Stage Single-Step Positivity-Preserving Finite Difference WENO Method for the Compressible Euler Equations

作者：Seal David C; Tang Qi; Xu Zhengfu; Christlieb Andrew J

来源：Journal of Scientific Computing, 2016, 68(1): 171-190.

DOI：10.1007/s10915-015-0134-0

• Hyperbolic conservation laws
• Lax-Wendroff
• Weighted essentially non-oscillatory
• Positivity-preserving

In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference weighted essentially non-oscillatory method. Time is discretized through a Lax-Wendroff procedure that is constructed from the Picard integral formulation of the partial differential equation. The method can be viewed as a modified flux approach, where a linear combination of a low-and high-order flux defines the numerical flux used for a single-step update. The coefficients of the linear combination are constructed by solving a simple optimization problem at each time step. The high-order flux itself is constructed through the use of Taylor series and the Cauchy-Kowalewski procedure that incorporates higher-order terms. Numerical results in one-and two-dimensions are presented.

• 出版日期2016-7
• 单位中国人民解放军海军大连舰艇学院