1. High-Resolution Viscous Terms Discretization and ILW Solid Wall Boundary Treatment for the Navier–Stokes Equations
- Author
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Francisco Augusto Aparecido Gomes, Chi-Wang Shu, Nicholas Dicati Pereira da Silva, and Rafael Brandão de Rezende Borges
- Subjects
Physics ,Discretization ,business.industry ,Applied Mathematics ,Numerical analysis ,Computational fluid dynamics ,Computer Science Applications ,Euler equations ,Boundary layer ,symbols.namesake ,Flow (mathematics) ,symbols ,Applied mathematics ,Oblique shock ,Navier–Stokes equations ,business - Abstract
Robust numerical methods for CFD applications, such as WENO schemes, quickly evolved in the past few decades. Together with the Inverse Lax–Wendroff (ILW) procedure, WENO ideas were also applied in the boundary treatment. Those methods are known for their high-resolution property, i.e., good representation of nonlinear phenomena, which is an important property in solving challenging engineering problems. In light of that, the objective of this work is to present a review of well-established high-resolution numerical methods to solve the Euler equations and adapt the Navier–Stokes viscous terms discretization and boundary treatment. To test the modifications, we employed the positivity-preserving Lax–Friedrichs splitting, multi-resolution WENO scheme, third-order strong stability preserving Runge–Kutta time discretization, and ILW boundary treatment. The first problems were simple flows with analytical solutions for accuracy tests. We also tested the accuracy with nontrivial phenomena in the vortex flow. Oblique shock and complicated flow structures were captured in the Rayleigh–Taylor instability and flow past a cylinder. We showed the discretization and boundary treatment can handle non-constant viscosity, are high-order, high-resolution, and behave similarly to the well-established numerical methods. Furthermore, the methods discussed here can preserve symmetry and no approximations regarding the boundary layer were made. Therefore, the discretization and boundary treatment can be considered when solving direct numerical simulations.
- Published
- 2021