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For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different…
This article proposes a new statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired from some Monte-Carlo algorithms used in linear transport physics, where virtual particles are…
The liquid-gas density ratio is a key property of multiphase flow methods to model real fluid systems. Here, a chemical-potential multiphase lattice Boltzmann method is constructed to realize extremely large density ratios. The simulations…
We establish the existence and uniqueness of mild solutions for the polyatomic ellipsoidal BGK model, which is a relaxation type kinetic model describing the evolution of polyatomic gaseous system at the mesoscopic level.
There are several approaches to describe flows with particles e.g. Lattice-Gas Automata (LGA), Lattice-Boltzmann method (LBM) or smoothed particle hydrodynamics (SPH). These approaches do not use fixed grids on which the Navier-Stokes…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
We study the boundary value problem of two stationary BGK-type models - the BGK model for fast chemical reaction and the BGK model for slow chemical reaction - and provide a unified argument to establish the existence and uniqueness of…
We present a new numerical algorithm based on a relative energy scaling for collisional kinetic equations allowing to study numerically their long time behavior, without the usual problems related to the change of scales in velocity…
Ideal gases can be modeled by the Boltzmann equation from statistical physics. Instead of trying to track the position and velocity of a large number of gas molecules, it is possible to describe the particles with a particle distribution…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
We consider the development of high order space and time numerical methods based on Implicit-Explicit (IMEX) multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which…
Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems,…
Driving an inertial many-body system out of equilibrium generates complex dynamics due to memory effects and the intricate relationships between the external driving force, internal forces, and transport effects. Understanding the…
A new method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a…
Accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and…
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), DSMC (Direct Simulation Monte Carlo), SPH (Smoothed Particle Hydrodynamics), PIC…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
In this paper, a unified gas kinetic scheme with adaptive velocity space (AUGKS) for multiscale flow transport will be developed. In near-equilibrium flow regions, particle distribution function is close to the Chapman-Enskog expansion and…