Recently, central methods combined with ENO limiting [1–3] have become very popular for hyperbolic problems. The main advantage is the simplicity of this method since no Riemann problem has to be solved. The only information necessary to know from the system under consideration is an estimate of the spectral radius of the linearization of the flux, corresponding to the maximum wave speeds of th...

We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interested in the behavior of the total variation (TV) of the approximate solution obtained with these methods. Our numerical results suggest that even though CWENO methods are not total variation diminish...

In this paper the relaxed, high-order, Multidimensional Optimal Order Detection (MOOD) framework is extended to simulation of compressible multicomponent flows on unstructured meshes. The diffuse interface methods (DIM) paradigm used that employs a five-equation model. implementation performed in open-source high-order flow solver UCNS3D. CWENO spatial discretisation selected due its reduced co...

We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interested in the behavior of the total variation (TV) of the approximate solution obtained with these methods. Our numerical results suggest that even though CWENO methods are not total variation diminish...

Until recently, numerical simulations of discontinuities in highly super-Alfvénic plasmas have been severely limited by comparatively crude resolution and accuracy. Significant progress in the numerical simulation of such plasmas was achieved with the recently implemented Central Weighted Essentially Non-Oscillatory (CWENO) scheme. Combining this technique with that of adaptive mesh refinement ...

The aim of this work is to develop a well-balanced Central Weighted Essentially Non Oscillatory (CWENO) method, fourth-order accurate in space and time, for shallow water system of balance laws with bed slope source term. Time accuracy is obtained applying a Runge-Kutta scheme (RK), coupled with the Natural Continuous Extension (NCE) approach. Space accuracy is obtained using WENO reconstructio...

Here we present a new, semidiscrete, central scheme for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The method presented in this paper is an extension of the centrally weighted non-oscillatory schemes (Cweno) presented in [7], [5] and [6]. The method suggested in this manuscript is derived independently of the order of the scheme. The gain in this new meth...

We present a new third-order essentially non-oscillatory central scheme for approximating solutions of twodimensional hyperbolic conservation laws. Our scheme is based on a two-dimensional extension of the centered weighted essentially non-oscillatory (CWENO) reconstruction we presented in Levy et al. [3]. This is a “true” 2D method; it is not based on a direction-by-direction approach. Our met...

Abstract In this paper we extend the application of unstructured high-order finite-volume central-weighted essentially non-oscillatory (CWENO) schemes to multicomponent flows using interface capturing paradigm. The developed method achieves accurate solution in smooth regions, while providing oscillation free solutions at discontinuous regions. are inherently compact sense that central stencils...