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...

Abstract In this short article, we respond to a Commentary by Maack et al. (Environ Sci Eur 34:24, 2022) in which they challenge recommendations Leverett 33:133, 2021) for setting an aquatic Environmental Quality Standard (EQS) the pharmaceutical diclofenac. recommend use of results from stream mesocosm study as main point departure EQS and dismiss Species Sensitivity Distribution (SSD) contain...

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...

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...

[1] The influence of aquifer property correlation on multiphase fluid migration and entrapment was explored through the use of correlated and uncorrelated porosity, permeability, and capillary pressure-saturation (Pc-Sat) parameter fields in a crosssectional numerical multiphase flow model. Data collected from core samples in a nonuniform sandy aquifer were used to generate three-dimensional aq...