Related papers: A sign preserving WENO reconstruction method
In this work, a framework to construct arbitrarily high-order low-dissipation shock-capturing schemes with flexible and controllable nonlinear dissipation for convection-dominated problems is proposed. While a set of candidate stencils of…
The reconstruction of images from a small number of projections using the maximum-entropy method (MEM) with the Shannon entropy is considered. MEM provides higher-quality image reconstruction for sources with extended components than 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…
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…
In this paper, we intend to use a B-spline quasi-interpolation (BSQI) technique to develop higher order hybrid schemes for conservation laws. As a first step, we develop cubic and quintic B-spline quasi-interpolation based numerical methods…
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…
In this paper, we develop parametrized positivity satisfying flux limiters for the high order finite difference Runge-Kutta weighted essentially non-oscillatory (WENO) scheme solving compressible Euler equations to maintain positive density…
We develop a positivity-preserving finite difference WENO scheme for the Ten-Moment equations with body forces acting as a source in the momentum and energy equations. A positive forward Euler scheme under a CFL condition is first…
The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…
This paper focuses on the numerical approximation of the solutions of non-local conservation laws in one space dimension. These equations are motivated by two distinct applications, namely a traffic flow model in which the mean velocity…
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…
We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is…
This paper proposes a new class of mass or energy conservative numerical schemes for the generalized Benjamin-Ono (BO) equation on the whole real line with arbitrarily high-order accuracy in time. The spatial discretization is achieved by…
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…
Applying high-order finite-difference schemes, like the extensively used linear-upwind or WENO schemes, to curvilinear grids can be problematic. The geometrically induced error from grid Jacobian and metrics evaluation can pollute the flow…
In simulations of compressible flows, the conservative finite difference method (FDM) based on the nonlinear upwind schemes, e.g. WENO5, might violate free-stream preserving (FP), due to the loss of the geometric conservation law (GCL)…
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…
Many interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use implicit time integration. Implicit integration…
We have proposed a new High Resolution Shock Capturing (HRSC) scheme for Special Relativistic Hydrodynamics (SRHD) based on the semidiscrete central Godunov-type schemes and a modified Weighted Essentially Non-oscillatory (WENO) data…
Finite volume methods are popular tools for solving time-dependent partial differential equations, especially hyperbolic conservation laws. Over the past 40 years a popular way of enlarging their robustness was the enforcement of global or…