Related papers: A new mapped WENO scheme using order-preserving ma…
We develop a simple, high-order, conservative and robust positivity-preserving sweeping procedure for the density and the nonlinear pressure function in the compressible Euler equations. Using the scaling limiter in Zhang and Shu (2010), we…
In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristic-wise approach, the scheme switches the numerical flux of each characteristic…
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used…
Due to its excellent shock-capturing capability and high resolution, the WENO scheme family has been widely used in varieties of compressive flow simulation. However, for problems containing strong shocks and contact discontinuities, such…
High order fast sweeping methods for efficiently solving steady state solutions of hyperbolic PDEs were not available yet on unstructured meshes. In this paper, we extend high order fast sweeping methods to unstructured triangular meshes by…
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…
This paper introduces an effcient class of adaptive stencil extension reconstruction methods based on a discontinuity feedback factor, addressing the challenges of weak robustness and high computational cost in high-order schemes,…
The shock instability problem commonly arises in flow simulations involving strong shocks, particularly when employing high-order schemes, limiting their applications in hypersonic flow simulations. This study focuses on exploring the…
The high-order gas-kinetic scheme(HGKS) with WENO spatial reconstruction method has been extensively validated through many numerical experiments, demonstrating its superior accuracy efficiency, and robustness. Compared with WENO class…
A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin…
The lack of smoothness is a common feature of weak solutions of nonlinear hyperbolic equations and is a crucial issue in their approximation. This has motivated several efforts to define appropriate indicators, based on the values of the…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws are extremely popular because, for multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume…
In this paper, we propose a hybrid finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws. The zeroth-order and the first-order moments are used in the…
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient…
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 adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). However when the spatial dimensions are high, the number of…
As we found previously, when critical points occur within grid intervals, the accuracy relations of smoothness indicators of WENO-JS would differ from that assuming critical points occurring on grid nodes, and accordingly the global…
To address the order degradation at critical points in the WENO3-Z scheme, some improvements have been proposed , but these approaches generally fail to consider the occurrence of critical points at arbitrary positions within grid…
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…