Related papers: Numerical simulation of nonlinear continuity equat…
We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of…
As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulation on fine spatial grids, we develop a new numerical method…
We propose a novel, highly efficient, mean-reverting-SAV-BDF2-based, long-time unconditionally stable numerical scheme for a class of finite-dimensional nonlinear models important in geophysical fluid dynamics. The scheme is highly…
We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…
We develop robust and scalable fully implicit nonlinear finite element solvers for the simulations of biological transportation networks driven by the gradient flow minimization of a non-convex energy cost functional. Our approach employs a…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
Recent advancements of intermediate-scale quantum processors have triggered tremendous interest in the exploration of practical quantum advantage. The simulation of fluid dynamics, a highly challenging problem in classical physics but vital…
The goal of this thesis is the development and implementation of a non-perturbative solution method for Wegner's flow equations. We show that a parameterization of the flowing Hamiltonian in terms of a scalar function allows the flow…
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
In this paper, we propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs). From a perspective of physical simulation, we redefine the problem of approximating the gradient flow utilizing…
The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel…
As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure. These systems are associated with non-increasing entropy…
In this paper, we consider numerical approximation of constrained gradient flows of planar closed curves, including the Willmore and the Helfrich flows. These equations have energy dissipation and the latter has conservation properties due…
This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic…
Gaseous flows under an external force are intrinsically defined by their multi-scale nature due to the large variation of densities along the forcing direction. Devising a numerical method capable of accurately and efficiently solving…
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…