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In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media. We will present the…
We present an energy-stable scheme for numerically approximating the governing equations for incompressible two-phase flows with different densities and dynamic viscosities for the two fluids. The proposed scheme employs a scalar-valued…
This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
We construct efficient original-energy-dissipative schemes for the Navier-Stokes-Darcy model and related two-phase flows using a prediction-correction framework. A new relaxation technique is incorporated in the correction step to guarantee…
In this paper, we design, analyze, and numerically validate positive and energy-dissipating schemes for solving the time-dependent multi-dimensional system of Poisson-Nernst-Planck (PNP) equations, which has found much use in the modeling…
We address in this paper a model for the simulation of turbulent deflagrations in industrial applications. The flow is governed by the Euler equations for a variable composition mixture and the combustion modelling is based on a…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…
The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can…
In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three…
We develop unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad \mathbb{R}^N\times(0,T), $$…
In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…
In this paper, we develop a novel staggered mesh (SM) approach for general nonlinear dissipative systems with arbitrary energy distributions (including cases with known or unknown energy lower bounds). Based on this framework, we propose…
This paper proposes a decoupled numerical scheme of the time-dependent Ginzburg--Landau equations under the temporal gauge. For the magnetic potential and the order parameter, the discrete scheme adopts the second type Ned${\rm…
In this paper, we propose and analyze a positivity-preserving, energy stable numerical scheme for certain type reaction-diffusion systems involving the Law of Mass Action with the detailed balance condition. The numerical scheme is…
In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on…