High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD
نویسنده
چکیده
In recent years high order numerical methods have been widely used in computational uid dynamics (CFD), to e ectively resolve complex ow features using meshes which are reasonable for today's computers. In this paper we review and compare three types of high order methods being used in CFD, namely the weighted essentially non-oscillatory (WENO) nite di erence methods, the WENO nite volume methods, and the discontinuous Galerkin (DG) nite element methods. We summarize the main features of these methods, from a practical user's point of view, indicate their applicability and relative strength, and show a few selected numerical examples to demonstrate their performance on illustrative model CFD problems.
منابع مشابه
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
In [19, 20, 22], we constructed uniformly high order accurate discontinuous Galerkin (DG) which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. The technique also applies to high order accurate finite volume schemes. In this paper, we show an extension of this framework to construct positivity-preserving high order essentially non-oscillatory (E...
متن کاملHigh order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, n...
متن کاملFinal Report of NASA Langley Grant NCC1-01035 Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows
methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present...
متن کاملHermite WENO schemes and their application as limiters for Runge–Kutta discontinuous Galerkin method: one-dimensional case
In this paper, a class of fifth-order weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one-dimensional nonlinear hyperbolic conservation law systems is presented. The construction of HWENO schemes is based on a finite volume formulation, Hermite interpolation, and nonlinearly stable Runge–Kutta methods. The idea o...
متن کاملThe multi-dimensional limiters for discontinuous Galerkin method on unstructured grids
Accuracy-preserving and non-oscillatory shock-capturing technique is the bottle neck in the development of discontinuous Galerkin method. Inspired by the success of the k-exact WENO limiters for high order finite volume methods, this paper generalize the k-exact WENO limiter to discontinuous Galerkin methods. Also several improvements are put forward to keep the compactness and high-order accur...
متن کامل