Related papers: Structure preserving schemes for a class of Wasser…
A simple scheme for incompressible, constant density flows is presented, which avoids odd-even decoupling for the Laplacian on a collocated grids. Energy stability is implied by maintaining strict energy conservation. Momentum is conserved.…
Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of…
The Swift-Hohenberg equation as a central nonlinear model in modern physics has a gradient flow structure. Here we introduce fully discrete discontinuous Galerkin (DG) schemes for a class of fourth order gradient flow problems, including…
We develop a new finite difference scheme for the Maxwell-Stefan diffusion system. The scheme is conservative, energy stable and positivity-preserving. These nice properties stem from a variational structure and are proved by reformulating…
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…
We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…
A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…
We design and analyse a semi-implicit finite volume scheme for the two-dimensional rotating shallow water (RSW) equations that is energy stable, well-balanced (capable of preserving discrete geostrophic steady states), consistent, and…
A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…
We present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail. Although numerical methods for geometric flows have been used frequently in axisymmetric settings,…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
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 consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
This paper is concerned with a rigorous convergence analysis of a fully discrete Lagrangian scheme for the Hele-Shaw flow, which is the fourth order thin-film equation with linear mobility in one space dimension. The discretization is based…
In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is achieved by first conditioning the underlying stochastic…
We derive mixed finite element discretizations of a cold relativistics fluid model from approximations of the Poisson bracket that preserve mass, energy and the divergence constraints. For time-discretization we derive an implicit…
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metric spaces. We first review some examples of gradient flows…
Central finite difference schemes have long been avoided in the context of two-phase flows for the advection of the phase indicator function due to numerical overshoots and undershoots associated with their dispersion errors. We will show…