Related papers: Numerical simulation of nonlinear continuity equat…
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…
We study a system of two continuity equations with nonlocal velocity fields using interaction potentials of both attractive and repulsive Morse type. Such a system is of interest in many contexts in multi-population modelling. We prove…
Nonlinear diffusion equations of spectral transfer are systematically derived for anisotropic magnetohydrodynamics in the regime of wave turbulence. The background of the analysis is the asymptotic Alfv\'en wave turbulence equations from…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…
We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…
We present a numerical scheme for solving a sixth-order Cahn-Hilliard type equation that captures the dynamics of phase transitions in a ternary mixture consisting of two immiscible fluids and a surface active molecule that is amphiphilic.…
We develop a method for modeling and simulating a class of two-phase flows consisting of two immiscible incompressible dielectric fluids and their interactions with imposed external electric fields in two and three dimensions. We first…
We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an EDI formulation of our PDE and prove that under some…
We study the particle method to approximate the gradient flow on the $L^p$-Wasserstein space. This method relies on the discretization of the energy introduced by [3] via nonoverlapping balls centered at the particles and preserves the…
A numerical explicit method to evaluates transient solutions of linear partial differential non-homogeneous equation with constant coefficients is proposed.
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin,…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
Equilibrium statistical mechanics tools have been developed to obtain indications about the natural tendencies of nonlinear energy transfers in two-dimensional and quasi two-dimensional flows like rotating and stratified flows in…