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A system of high-order adaptive multiresolution wavelet collocation upwind schemes are developed for the solution of hyperbolic conservation laws. A couple of asymmetrical wavelet bases with interpolation property are built to realize the…
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial…
In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured…
In this paper, we combine the nonlinear HWENO reconstruction in \cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilton-Jacobi equations in a novel HWENO framework recently…
Weighted compact nonlinear schemes (WCNS) [Deng and Zhang, JCP 165(2000): 22-44] were developed to improve the performance of the compact high-order nonlinear schemes (CNS) by utilizing the weighting technique originally designed for WENO…
In this paper, a high-order multi-dimensional gas-kinetic scheme is presented for both inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation. Compared with the traditional ALE method, the flow variables are updated…
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…
We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage, single-step, maintains a discrete divergence-free condition on the magnetic field,…
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…
In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO…
We present a new approach to stabilizing high-order Runge-Kutta discontinuous Galerkin (RKDG) schemes using weighted essentially non-oscillatory (WENO) reconstructions in the context of hyperbolic conservation laws. In contrast to RKDG…
The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show…
We construct a new compact semi-explicit three-level in time fourth-order finite-difference scheme for numerical solving the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are…
Accurate and efficient reconstruction techniques are essential in multiresolution analysis and image compression, particularly when the data are represented as cell averages. In this work, we present a non-separable progressive multivariate…
The main aim of this work is not to improve any existing non-linear weight but to give a generalized framework for the construction of non-linear weights to get non-oscillatory third order WENO schemes. It is done by imposing necessary…
This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…
This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method…
In this paper we introduce a general framework for defining and studying essentially non-oscillatory reconstruction procedures of arbitrarily high order accuracy, interpolating data in a central stencil around a given computational cell…
Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the…
The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for the…