A family of fourth-order entropy stable nonoscillatory spectral collocation schemes for the 1-D Navier-Stokes equations

详细信息    查看全文

• 作者：Nail K. Yamaleev^a ; ^{nyamalee@odu.edu} ; Mark H. Carpenter^b
• 关键词：Summation-by-parts (SBP) operators ; Entropy stability ; Spectral collocation methods ; Weighted essentially nonoscillatory (WENO) schemes ; The Navier&ndash ; Stokes equations
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：331
• 期：Complete
• 页码：90-107
• 全文大小：729 K
• 卷排序：331

文摘

High-order numerical methods that satisfy a discrete analog of the entropy inequality are uncommon. Indeed, no proofs of nonlinear entropy stability currently exist for high-order weighted essentially nonoscillatory (WENO) finite volume or weak-form finite element methods. Herein, a new family of fourth-order WENO spectral collocation schemes is developed, that are nonlinearly entropy stable for the one-dimensional compressible Navier–Stokes equations. Individual spectral elements are coupled using penalty type interface conditions. The resulting entropy stable WENO spectral collocation scheme achieves design order accuracy, maintains the WENO stencil biasing properties across element interfaces, and satisfies the summation-by-parts (SBP) operator convention, thereby ensuring nonlinear entropy stability in a diagonal norm. Numerical results demonstrating accuracy and nonoscillatory properties of the new scheme are presented for the one-dimensional Euler and Navier–Stokes equations for both continuous and discontinuous compressible flows.