Related papers: Conservative numerical schemes with optimal disper…
This paper proposes a second-order accurate numerical scheme for the Patlak-Keller-Segel system with various mobilities for the description of chemotaxis. Formulated in a variational structure, the entropy part is novelly discretized by a…
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov--Fokker--Planck system coupled with Poisson or Amp\`ere equation. Splitting methods…
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…
This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast algebraic solvers. We present details for the second order…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
The shear shallow water model is an extension of the classical shallow water model to include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non-conservative products. We develop a high-order entropy…
High-frequency wave propagation in near-inertial wave shear has been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave-breaking. We compare idealized ray…
Numerical schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence, numerical simulations of wave-like systems lacking proper handling of these…
We propose a new fully-discretized finite difference scheme for a quantum diffusion equation, in both one and two dimensions. This is the first fully-discretized scheme with proven positivity-preserving and energy stable properties using…
We present error estimates for four unconditionally energy stable numerical schemes developed for solving Allen-Cahn equations with nonlocal constraints. The schemes are linear and second order in time and space, designed based on the…
Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
We use the general framework of summation-by-parts operators to construct conservative, energy-stable, and well-balanced semidiscretizations of two different nonlinear systems of dispersive shallow water equations with varying bathymetry:…
A challenge in physical oceanography is quantifying the energy content of waves and balanced flows and the fluxes that connect these reservoirs with their sources and sinks. Methodological limitations have prevented decompositions for…
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by…
The equations of Lagrangian gas dynamics fall into the larger class of overdetermined hyperbolic and thermodynamically compatible (HTC) systems of partial differential equations. They satisfy an entropy inequality (second principle of…
Fast and accurate structural dynamics analysis is important for structural design and damage assessment. Structural dynamics analysis leveraging machine learning techniques has become a popular research focus in recent years. Although the…
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…