Related papers: Mechanics-based solution verification for porous m…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. We have studied numerical methods for PME by an energetic variational approach in [C. Duan et al, J. Comput. Phys., 385 (2019) 13-32], where the…
This paper investigates the existence of weak solutions to two problems set of elliptic equations in adjoining domains, with Beavers--Joseph--Saffman and regularized Butler--Volmer boundary conditions being prescribed on the common…
In this paper we introduce a novel Neural Networks-based approach for approximating solutions to the (2D) incompressible Navier--Stokes equations, which is an extension of so called Deep Random Vortex Methods (DRVM), that does not require…
A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field formulation of the Darcy law for the description of the hydraulic head on the fractures and uses a cost…
We develop a class of mixed virtual volume methods for elliptic problems on polygonal/polyhedral grids. Unlike the mixed virtual element methods introduced in \cite{brezzi2014basic,da2016mixed}, our methods are reduced to symmetric,…
We study a general convergence theory for the numerical solutions of compressible viscous and electrically conducting fluids with a focus on numerical schemes that preserve the divergence free property of magnetic field exactly. Our…
In numerical ocean models coast lines change the direction from one grid cell to its neighbor and the value for viscosity is set to be as small as possible. Therefore, model simulations are not converged with resolution and boundary…
Physics-governed models are increasingly paired with machine learning for accelerated predictions, yet most "physics--informed" formulations treat the governing equations as a penalty loss whose scale and meaning are set by heuristic…
We investigate the blowup criterion of the barotropic compressible viscous fluids for the Cauchy problem, Dirichlet problem and Navier-slip boundary condition. The main novelty of this paper is two-fold: First, for the Cauchy problem and…
Immiscible fluid displacement in porous media occurs in several natural and industrial processes. For example, during petroleum extraction from porous rock reservoirs, water is used to displace oil. In this paper, we investigate primary…
Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…
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…
In this paper we introduce and analyze, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of…
Particle-in-cell methods with stochastic collision models are commonly used to simulate collisional plasma dynamics, with applications ranging from hypersonic flight to semiconductor manufacturing. Code verification of such methods is…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology and medicine. Despite more than 150 years since the publication of Darcy's linear…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting…
Transport phenomena in porous media are commonplace in our daily lives. Examples and applications include heat and moisture transport in soils, baking and drying of food stuffs, curing of cement, and evaporation of fuels in wild fires. Of…