Related papers: A novel method for constructing high accurate and …
We present adaptive finite difference ENO/WENO methods by adopting infinitely smooth radial basis functions (RBFs). This is a direct extension of the non-polynomial finite volume ENO/WENO method proposed by authors in \cite{GuoJung} to the…
This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an…
The numerical simulation of supersonic complex flow problems demands capabilities in identifying multiscale structures and capturing shocks, imposing stringent requirements on the numerical scheme. The capability to identify multiscale…
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…
A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO…
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 situations where a wide range of flow scales are involved, the nonlinear scheme used should be capable of both shock capturing and low-dissipation.Most of the existing WCNS schemes are too dissipative because the weights deviate from…
We propose a third-order WENO reconstruction which satisfies the sign property, required for constructing high resolution entropy stable finite difference scheme for conservation laws. The reconstruction technique, which is termed as…
The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equations, or the design of curves and surfaces. Numerous methods…
We present a novel mapping approach for WENO schemes through the use of an approximate constant mapping function which is constructed by employing an approximation of the classic signum function. The new approximate constant mapping…
Shallow water moment equations are reduced-order models for free-surface flows that allow to represent vertical variations of the velocity profile at the expense of additional evolution equations for a number of additional variables, so…
In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic…
In an attempt to investigate the structures of ultra-relativistic jets injected into the intracluster medium (ICM) and the associated flow dynamics, such as shocks, velocity shear, and turbulence, we have developed a new special…
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…
This paper is concerned with high-order numerical methods for hyperbolic systems of balance laws. Such methods are typically based on high-order piecewise polynomial reconstructions (interpolations) of the computed discrete quantities.…
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…
We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov-Poisson system, the…
In our previous work [29], we proposed a class of high-order asymptotic preserving (AP) finite difference weighted essentially non-oscillatory (WENO) schemes for solving the shallow water equations (SWEs) with bottom topography and Manning…
In this article we present a modification of the algorithm for data discretized in the point values introduced in [S. Amat, J. Ruiz, C.-W. Shu, On a new WENO algorithm of order 2r with improved accuracy close to discontinuities, App. Math.…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…