On the idea of mapped WENO scheme, properties mapping methods are analyzed, uncertainties in development investigated, and new piecewise rational mappings proposed. Based on our former understandings, i.e. at endpoints {0, 1} tending to identity mapping, a so-called Cn,m condition is summarized for function development. Uncertainties, i.e., whether pattern would make scheme behave like or ENO, ...

This paper reports a numerical study on the effect of turbulence on the detonation wave properties. The analysis is based on the integration of the chemically reactive Navier– Stokes equations using a Runge–Kutta scheme and a fifth-order WENO spatial discretization. We perform a direct numerical simulation (DNS) of the fluid-mechanics equations in three dimensions to determine the fine-scale ev...

The positivity and accuracy properties of the widely used ENO and WENO methods are considered by undertaking an analysis based upon data-bounded polynomial methods. The positivity preserving approach of Berzins based upon data-bounded polynomial interpolants is generalized to arbitrary meshes. This makes it possible to prove positivity conditions for ENO Methods by using a derivation based on s...

The Laboratory's main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. Solutions to hyperbolic conservation laws are often characterized by a large range of length scales as well as discontinuities. Standard nonlinear finite-difference schemes, such as the WENO sche...

We derive Godunov-type semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. High-order schemes are then obtained by combining our new numerical fluxes with high-order WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone in certain cases. The accuracy and high-resolution properties of our scheme are demonstrated in a variety of nume...

In this paper, a hybrid numerical flux scheme of low diffusion ECUSP (LDE) and HLL scheme is proposed by decomposing the cell-face normal vector. In the direction normal to shocks, the HLL scheme is applied to suppress carbuncles, in the other direction, the ECUSP scheme is implemented to keep low numerical diffusion. The new scheme with fifth-order WENO reconstruction is tested by using severa...