Related papers: A Class of High Resolution Shock Capturing Schemes…
In this paper, we introduce a hyperbolic model for entropy dissipative system of viscous conservation laws via a flux relaxation approach. We develop numerical schemes for the resulting hyperbolic relaxation system by employing the…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
A new approach to prevent spurious behavior caused by conventional shock-capturing schemes when solving stiff detonation waves problems is introduced in the present work. Due to smearing of discontinuous solution by the excessive numerical…
We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle…
This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…
A class of high-order shock-capturing schemes, P$_n$T$_m$-BVD (Deng et al., J. Comp. Phys., 386:323-349, 2019; Comput. & Fluids, 200:104433, 2020.) schemes, have been devised to solve the Euler equations with substantially reduced numerical…
We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of a scalar hyperbolic conservation law. We begin with sufficient conditions for a space discretization to be bound…
In this work we present a framework for enforcing discrete maximum principles in discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to scalar conservation laws as well as hyperbolic systems. Our methodology…
This paper aims at developing exactly energy-conservative and structure-preserving finite volume schemes for the discretisation of first-order symmetric-hyperbolic and thermodynamically compatible (SHTC) systems of partial differential…
Structure-preserving finite-difference schemes for general nonlinear fourth-order parabolic equations on the one-dimensional torus are derived. Examples include the thin-film and the Derrida-Lebowitz-Speer-Spohn equations. The schemes…
Solving compressible flows containing discontinuities remains a major challenge for numerical methods especially on unstructured grids. Thus in this work, we make contributions to shock capturing schemes on unstructured grids with aim of…
In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
The simulation of transcritical flows remains challenging due to strong thermodynamic nonlinearities that induce spurious pressure oscillations in conventional schemes.While primitive-variable formulations offer improved robustness under…
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-discrete version of the proposed method is based on a technique…
We present a class of hybrid FD-FV (finite difference and finite volume) methods for solving general hyperbolic conservation laws written in first-order form. The presentation focuses on one- and two-dimensional Cartesian grids; however,…
Our goal is to develop a flux limiter of the Flux-Corrected Transport method for a nonconservative convection-diffusion equation. For this, we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a…
A second-order total variation diminishing (TVD) method with variable flux limiters is proposed to overcome the non-realizability issue, which has been one of major obstacles in applying the conventional second-order TVD schemes to the…
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…