טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentSingh Vikram
SubjectStabilization of High-Order Flux-Reconstruction Scheme for
Wall-Modeled Implicit Large Eddy Simulation
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Steven Howard Frankel


Abstract

Traditionally, industrial Computational Fluid Dynamics (CFD) codes have used low

order finite volume methods. This is due to the fact that low-order methods allow both

numerical robustness and flexibility in terms of geometries. But low-order methods are also generally more dissipative which is undesirable for transitional or highly turbulent, vorticity dominated flows. This has lead to the recent trend towards development of high order methods in CFD. High-order methods have been shown to provide more accurate solutions for the same number of degrees of freedom. In addition, extending high order methods to unstructured grids is also desirable since it allows flexibility in terms of geometries over which simulations are done. One promising method to address this problem is the flux reconstruction (FR) method.

The flux reconstruction (FR) method was first proposed as a unified and intuitive

approach to high-order unstructured computational fluid dynamics (CFD) solvers. The

ease of implementation and the high order nature of flux reconstruction for complex

geometries makes it advantageous for simulating fluid flows. However, high order meth- ods suffer from aliasing instabilities. This is an especially acute problem when grids used for the simulations are under-resolved. Split forms are an attractive solution since they can often be modified to satisfy non-linear stability properties such as entropy. In this work, we first introduce the method and its implementation for the compressible Navier Stokes equations. We first show validation using some simple cases. Next we introduce split forms and show how they contribute towards more stable simulations. We develop some new split forms to introduce properties that we want in the discretiza- tion. Finally we address implicit large eddy simulation (ILES) and wall modeling for high Reynolds’ number flows.