Related papers: Barotropic-Baroclinic Splitting for Multilayer Sha…
A fundamental problem of non-equilibrium statistical mechanics is the derivation of macroscopic transport equations in the hydrodynamic limit. The rigorous study of such limits requires detailed information about rates of convergence to…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group…
We show that discrete schemes developed for lattice hydrodynamics provide an elegant and physically transparent way of deriving Laplacians with isotropic discretisation error. Isotropy is guaranteed whenever the Laplacian weights follow…
We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in…
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…
Recent research has shown that motile cells can adapt their mode of propulsion depending on the environment in which they find themselves. One mode is swimming by blebbing or other shape changes, and in this paper we analyze a class of…
In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that…
Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…
Methods for building a consistent interface between hydrodynamic and simulation modules is presented. These methods account for the backflow across the hydrodynamic/simulation hyper-surface. The algorithms are efficient, relatively…
A numerical method is proposed for solving the two layer shallow water equations with variable bathymetry in one dimension based on high-resolution f-wave-propagation finite volume methods. The method splits the jump in the fluxes and…
Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics (MHD) both in the ideal and resistive cases, and in the presence of viscosity. The method is deduced from…
In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…
We extend exploration of potential vorticity instabilities in cold astrophysical disks whose mean states are baroclinic. In particular, we seek to demonstrate the potential existence of traditional baroclinic instabilities of meteorological…
The mean state of the atmosphere and ocean is set through a balance between external forcing (winds, radiation, heat and freshwater fluxes) and the emergent turbulence, which transfers energy to dissipative structures. The forcing gives…
This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning…
From the microscopic view, the energy partition between two fission fragments are associated with the splitting of wave functions of an entangled fissioning system, in contrast to most fission models using an explicit statistical partition…