相关论文: An Upwind Generalized Finite Difference Method for…

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…

In this work, we present an upscaled model for mixed dimensional coupled flow problem in fractured porous media. We consider both embedded and discrete fracture models (EFM and DFM) as fine scale models which contain coupled system of…

A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…

In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG…

In this work, we introduce two novel reformulations of a recent weakly hyperbolic model for two-phase flow with surface tension. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a…

We extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are…

In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…

The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…

Traditional two level upscaling techniques suffer from a high offline cost when the coarse grid size is much larger than the fine grid size. Thus, multilevel methods are desirable for problems with complex heterogeneities and high contrast.…

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…

A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each…

Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…

Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…

We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step…

Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…

In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the…

Lack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate…

A so-called grid-overlay finite difference method (GoFD) was proposed recently for the numerical solution of homogeneous Dirichlet boundary value problems of the fractional Laplacian on arbitrary bounded domains. It was shown to have…

We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…