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...

In this paper, we introduce an improved version of mapped weighted essentially nonoscillatory (WENO) schemes for solving Hamiton-Jacobi equations. To this end, we first discuss new smoothness indicators for WENO construction. Then the new smoothness indicators are combined with the mapping function developed by Henrick et. al. [24]. The proposed scheme yields fifth-order accuracy in smooth regi...

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 metho...

This paper presents a hybrid finite-difference/weighted essentially non-oscillatory (WENO) method for large-eddy simulation of compressible flows with low-numerical dissipation schemes and structured adaptive mesh refinement (SAMR). A conservative flux-based approach is described, encompassing the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered...

We have proposed a new High Resolution Shock Capturing (HRSC) scheme for Special Relativistic Hydrodynamics (SRHD) based on the semidiscrete central Godunov-type schemes and a modified Weighted Essentially Non-oscillatory (WENO) data reconstruction algorithm. This is the first application of the semidiscrete central schemes with high order WENO data reconstruction to the SRHD equations. This me...

To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091–3120] to convection diffusion equations, we propose a nonconventional high order finite volume weighted essentially nonoscillatory (WENO) scheme which can be proved maximum-principle-satisfying. Two-dimensional extensions are straightforwa...

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high order positivity-preserving finite difference WENO methods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, under the constrained transport (CT...

This paper investigates the feasibility of a high order finite difference weighted essentially nonoscillatory(WENO) scheme for large eddy simulations(LES) with implicit subgrid scale model. In this paper, the 5th-order WENO scheme with a conservative 4th-order central differencing for viscous terms are used to simulate the flow past a circular cylinder at ReD = 3900. The turbulent effects near ...

The accurate prediction of helicopter rotor blade–vortex interaction (BVI) noise is challenging. This paper presents an implementation the seventh-order improved weighted essentially non-oscillatory (WENO-Z) scheme for predicting BVI using a high-resolution numerical method based on Reynolds-averaged Navier–Stokes and Ffowcs Williams–Hawkings equations. WENO-Z utilized to minimize inherent diss...

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for shallow water equations under arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The WENO reconstruction is adopted on moving meshes, which distinguishes smooth, non-smooth, and transition stencils by a simple smoothness detector. To maintain positivi...