Physical phenomenon in nature is generally simulated by partial differential equations. Among different sorts of equations, the problem two-phase flow porous media has been paid intense attention. As a promising direction, physics-informed neural networks shed new light on solution However, current networks’ ability to learn equations relies adding artificial diffusion or using prior knowledge ...

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 oneand two-dimensional Cartesian grids; however, the generalization to higher dimensions is straightforward. These methods use both cell-averaged values and nodal values as dependent variables to discretize the...

In this work we investigate the advantages of multiscale methods in Petrov-Galerkin (PG) formulation in a general framework. The framework is subject to a localized orthogonal decomposition of a high dimensional solution space into a low dimensional multiscale space and a high dimensional remainder space with negligible fine scale information. As a model problem we consider the Poisson problem....

We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discontinuous solutions. Thanks to the mesh-less property of the RBFs, the method is suitable for non uniform grids and mesh adaptation. We focus o...

Fractured karstic carbonate reservoirs have obvious multi-scale characteristics and severe heterogeneity due to the development of abundant karst caves fractures with different scales. Darcy non-Darcy flows coexist this property. Therefore, selecting appropriate flow equations for regions in numerical simulation fluid flows, particularly two-phase multiphase is a critical topic. This paper comp...

We present semianalytical solutions for cocurrent displacements with some degree of countercurrent flow. The solution assumes a one-dimensional horizontal displacement of two immiscible incompressible fluids with arbitrary viscosities and saturation-dependent relative permeability and capillary pressures. We address the impact of the system length on the degree of countercurrent flow when there...

We present a numerical study of the scale up problem for the fractional ow function in the Buckley-Leverett equation for ow in porous media. The scale up problem is to deene an averaged equation by local spatial averages, mapping from a micro-physical description to a meso-physical description and from a ne discretization grid to a coarser one. Scale up leads to the closure problem, which is th...

We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discontinuous solutions. Thanks to the mesh-less property of the RBFs, the method is suitable for non-uniform grids and mesh adaptation. We focus o...

The paper presents the application of Control-Volume Finite Element (CVFE) method in simulation of multi-phase (water, oil, gas) flow through porous media. The numerical model developed using the CVFE method presents advantage in simulation of faulted reservoirs or simulation of complex geometry reservoir. Also, CVFE method can accurate represents the location of wells inside of reservoir, fact...

We study the large time asymptotic shock front speed in an inviscid Burgers equation with a spatially random flux function. This equation is a prototype for a class of scalar conservation laws with spatial random coefficents such as the wellknown Buckley-Leverett equation for two-phase flows, and the contaminant transport equation in groundwater flows. The initial condition is a shock located a...