Related papers: Lie group stability of finite difference schemes
The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper,…
In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the case of gradient flows, the schemes dissipate the free energy…
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…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
Symmetry principles underlie and guide scientific theory and research, from Curie's invariance formulation to modern applications across physics, chemistry, and mathematics. Building on a recent matrix Lie group measurement model, this…
We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present…
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: Firstly, as building blocks in the subcell flux…
The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the…
The relation between symmetries and local conservation laws, known as Noether's theorem, plays an important role in modern theoretical physics. As a discrete analog of the differentiable physical system, a good numerical scheme should admit…
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…
Research on numerical stability of difference equations has been quite intensive in the past century. The choice of difference schemes for the derivative terms in these equations contributes to a wide range of the stability analysis issues…
We describe high order accurate and stable fully-discrete finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…
There are several well-established approaches to constructing finite difference schemes that preserve global invariants of a given partial differential equation. However, few of these methods preserve more than one conservation law locally.…