Related papers: Space-time discretization for barotropic flow stem…
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…
We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for fluid and plasma equation, incorporating the recent advances to…
We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy-Green deformation…
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The…
We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for…
We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…
A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and the metric underlying the gradient flow are anisotropic,…
In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…
The Lagrangian, multi-dimensional, ideal, compressible gasdynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, $m^i$ (the Lagrangian mass coordinates) and time $t$ are the independent variables,…
Geometric flows, where an immersed manifold evolves in time according to its own geometry, exhibit important structural properties. For example, surface diffusion dissipates surface area while conserving volume; it is desirable to preserve…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with respect to a metric that generalizes martingale transport.…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation's gradient flow structure with respect to the Wasserstein distance. The scheme inherits…
We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization. We prove that our method is structure preserving in 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…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
We give a structure preserving spatio-temporal discretization for incompressible magnetohydrodynamics (MHD) on the sphere. Discretization in space is based on the theory of geometric quantization, which yields a spatially discretized…
In this paper, we study the behaviour at low Mach number of numerical schemes based on staggered discretizations for the barotropic Navier-Stokes equations. Three time discretizations are considered: the implicit-in-time scheme and two…
The paper considers one-dimensional flows of a polytropic gas in the Lagrangian coordinates in three cases: plain one-dimensional flows, radially symmetric flows and spherically symmetric flows. The one-dimensional flow of a polytropic gas…