Related papers: Invariant discretization schemes for the shallow-w…
Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction…
Spurious numerical mixing is a frequent phenomenon in ocean models. In this paper, we present an efficient and robust methodology that defines the vertical grid motion so that this mixing is reduced. This motion is defined as the solution…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
In this paper, we present a systematic framework to derive a Lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational approach. Such discrete energetic variational approaches are…
In this article we design a finite volume semi-implicit IMEX scheme for the incompressible Navier-Stokes equations on evolving Chimera meshes. We employ a time discretization technique that separates explicit and implicit terms which…
In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…
Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical…
We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…
Hydrodynamic cosmological simulations at present usually employ either the Lagrangian SPH technique, or Eulerian hydrodynamics on a Cartesian mesh with adaptive mesh refinement. Both of these methods have disadvantages that negatively…
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…
A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant…
In the recent paper by Bernardini et al. [J. Comput. Phys. 232 (2013), 1-6] the discrepancy in the performance of finite difference and spectral models for simulations of flows with a preferential direction of propagation was studied. In 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 work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive,…
This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…