Compressible reacting flows may display sharp spatial variation related to shocks, contact discontinuities or reactive zones embedded within relatively smooth regions. The presence of such phenomena emphasizes the relevance shock-capturing schemes as weighted essentially non-oscillatory (WENO) scheme an essential ingredient numerical solver. However, these are complex and have more computationa...

We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes, our method is based on reconstructing a piecewisepolynomial interpolant from cell-averages which is then advanced exactly in time. In the reconstruction step, we introduce a new third-order, compact, CWENO reconstruction,...

We present new thirdand fifth-order Godunov-type central schemes for approximating solutions of the Hamilton–Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme ...

High-order accurate shock-capturing schemes are capable of properly resolving discontinuities with correct wave speeds in single-fluid Riemann problems. However, when different fluids are present, oscillations develop at interfaces. A class of existing interface-capturing methods that suppress these oscillations is based on firstand second-order accurate reconstructions with Roe solvers. In thi...

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of ...

The usual geometrical-optics expansion of the solution for the Helmholtz equation of a point source in an inhomogeneous medium yields two equations: an eikonal equation for the traveltime function, and a transport equation for the amplitude function. However, two difficulties arise immediately: one is how to initialize the amplitude at the point source as the wavefield is singular there; the ot...

Abstract. The purpose of this work is to develop a methodology that achieves high order spatial discretization for compressible aerodynamic flows based on the spectral finite volume method for hyperbolic conservation laws. High order methods are necessary on the analysis of complex flows to reduce the number of mesh elements one would otherwise need if using traditional second-order schemes. In...

We investigate the achievable efficiency of both the time and the space discretisation methods used in Antares for mixed parabolic–hyperbolic problems. We show that the fifth order variant of WENO combined with a second order Runge–Kutta scheme is not only more accurate than standard first and second order schemes, but also more efficient taking the computation time into account. Then, we calcu...

A third-order Energy Stable Weighted Essentially Non–Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter (AIAA 2008–2876, 2008) was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables “energy stable” modifications for existing WENO s...