We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. WENO is a higher order accurate finite difference scheme designed for problems with piecewise smooth solutions containing discontinuities, and has been successful in application for problems involving bo...

Based on the Weighted Essential Non-Oscillatory (WENO) reconstruction for the macroscopic flow variables and the direct use of the corresponding gas distribution function of the NavierStokes (NS) solution, a high-order finite volume gas-kinetic scheme is constructed. Different from the previous high-order gas-kinetic method [Li, Xu, and Fu, A high-order gas-kinetic Navier-Stokes solver, J. Comp...

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...

We present a new multidimensional classical hydrodynamics code based on Semidiscrete Central Godunov-type schemes and high order Weighted Essentially Non-oscillatory (WENO) data reconstruction. This approach is a lot simpler and easier to implement than other Riemann solver based methods. The algorithm incorporates elements of the Piecewise Parabolic Method (PPM) in the reconstruction schemes t...

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, HamiltonJacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses onto diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These schemes are based on a suitable semilinear hyperboli...

In this paper, we consider the issue of convergence toward entropy solutions for high order finite volume weighted essentially non-oscillatory (WENO) scheme and discontinuous Galerkin (DG) finite element method approximating scalar nonconvex conservation laws. Although such high order nonlinearly stable schemes can usually converge to entropy solutions of convex conservation laws, convergence m...

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknow...