Related papers: Moment-based multi-resolution HWENO scheme for hyp…
In this paper, a compact and high order ADER (Arbitrary high order using DERivatives) scheme using the simple HWENO method (ADER-SHWENO) is proposed for hyperbolic conservation laws. The newly-developed method employs the Lax-Wendroff…
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…
We develop new more efficient A-WENO schemes for both hyperbolic systems of conservation laws and nonconservative hyperbolic systems. The new schemes are a very simple modification of the existing A-WENO schemes: They are obtained by a more…
A modified Weighted Essentially Non-Oscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the…
Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. Similar as other fast sweeping schemes, the key components of…
In this paper we generalize to non-uniform grids of quad-tree type the Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput., 2001), thus obtaining a truly two-dimensional non-oscillatory third order reconstruction with…
Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially…
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…
We construct an efficient class of increasingly high-order (up to 17th-order) essentially non-oscillatory schemes with multi-resolution (ENO-MR) for solving hyperbolic conservation laws. The candidate stencils for constructing ENO-MR…
Based on the solution formula method, a series of one-step fully-discrete schemes, such as FWENO/Full-WENO has been proposed. Storing the by-products conservative variables at the half points (grid center) and using them as interpolation…
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M.…
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…
In this paper, we propose to combine the fifth order Hermite weighted essentially non-oscillatory (HWENO) scheme and fast sweeping method (FSM) for the solution of the steady-state $S_{N}$ transport equation in the finite volume framework.…
A hybrid LDG-HWENO scheme is proposed for the numerical solution of KdV-type partial differential equations. It evolves the cell averages of the physical solution and its moments (a feature of Hermite WENO) while discretizes high order…
In this paper, we develop two finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and $\mu$-Degasperis-Procesi ($\mu$DP) equations, which contain…
High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…
We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus of this work is on nonlinear stabilization of continuous…
In this article we present the first better than second order accurate unstructured Lagrangian-type one-step WENO finite volume scheme for the solution of hyperbolic partial differential equations with non-conservative products. The 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…