Related papers: Space-time discretization for barotropic flow stem…
We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a…
We extend the general relativistic Lagrangian perturbation theory, recently developed for the formation of cosmic structures in a dust continuum, to the case of model universes containing a single fluid with a single-valued analytic…
We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants (mass and $L^2$-energy), while also maintaining discrete…
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
The equations of Lagrangian, ideal, one-dimensional (1D), compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate $m$ and time $t$ as independent variables, and in which the Eulerian position of…
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…
In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…
We present a consistent high-order staggered Lagrangian hydrodynamics framework designed to reconcile an underlying disparity in existing curvilinear formulations: the mismatch between quadrature-based "strong" mass conservation and the…
In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of…
High-order temporal discretizations for hyperbolic conservation laws have historically been formulated as either a method of lines (MOL) or a Lax-Wendroff method. In the MOL viewpoint, the partial differential equation is treated as a large…
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with…
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies…
This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional…
We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our discretization is based on a prescribed energy-dissipation law…
We consider the variational principle for the Lagrangian 1-form structure for long-range models of Calogero-Moser (CM) type. The multiform variational principle involves variations with respect to both the field variables as well as the…
This paper develops a geometric mechanics framework for the reduction of general relativistic hydrodynamic variational principles, from the variation of worldlines approach in 4D spacetime to 3-dimensional Eulerian descriptions. We consider…