Related papers: A High-Order Modified Finite Volume WENO Method on…

In this paper we analyze the weighted essentially non-oscillatory (WENO) schemes in the finite volume framework by examining the first step of the explicit third-order total variation diminishing Runge-Kutta method. The rationale for the…

This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…

In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO) framework recently developed in [24]. In particular, we…

Balsara (2001, J. Comput. Phys., 174, 614) showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes…

Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the…

We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid…

Weighted essentially non-oscillatory (WENO) reconstruction schemes are presented that preserve cylindrical symmetry for radial flows on an equal-angle polar mesh. These new WENO schemes are used with a Lagrangian discontinuous Galerkin (DG)…

We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-order flux splitting schemes introduced in [ E. F. Toro, M.…

Interfacial mass transfer of low-diffusive substances in an unsteady flow environment is marked by a very thin boundary layer at the interface and other regions with steep concentration gradients. A numerical scheme capable of resolving…

The spectral volume(SV) method constructs a high-order polynomial for SV based on the average value of control volume(CV), but for discontinuous problems, a limiter is required to mitigate oscillations. This paper presents a novel CV-based…

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is…

In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…

We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit:…

We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on moving 2D Voronoi meshes that…

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…

The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…

In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…

In this paper, a high order implicit Method of Line Transpose (MOL$^T$ ) method based on a weighted essentially non-oscillatory (WENO) methodology is developed for one-dimensional linear transport equations and further applied to the…

In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO…