Related papers: A Moving Mesh Method for Porous Medium Equation by…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the…
By using the Onsager variational principle as an approximation tool, we develop a new diffusion generated motion method for wetting problems. The method uses a signed distance function to represent the interface between the liquid and vapor…
We study numerical methods for porous media equation (PME). There are two important characteristics: the finite speed propagation of the free boundary and the potential waiting time, which make the problem not easy to handle. Based on…
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…
A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse…
In this paper, we present a systematic framework to derive a Lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational approach. Such discrete energetic variational approaches are…
Direct numerical simulation of microscale fluid--structure interactions in multicomponent and multiphase flows requires methods that can represent moving boundaries together with fields constrained to evolving interfaces. Diffuse-domain…
We introduce a new scheme for solving the non-regularized Porous Medium Equation. It is mass conserving and uses only positive unknown values. To address these typically conflicting features, we employ the eXtreme Mesh deformation approach…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…
A lack of regularity in the solution of the porous medium equation poses a serious challenge in its theoretical and numerical studies. A common strategy in theoretical studies is to utilize the pressure formulation of the equation where a…
A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170…
The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active systems,…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
In 1931, Onsager proposed a variational principle which has become the base of many kinetic equations for non-equilibrium systems. We have been showing that this principle is useful in obtaining approximate solutions for the kinetic…
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily…