Related papers: A splitting scheme for the quantum Liouville-BGK e…
Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…
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…
The advection-diffusion equation is simulated on a superconducting quantum computer via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive…
In this work, we theoretically and numerically discuss the time fractional subdiffusion-normal transport equation, which depicts a crossover from sub-diffusion (as $t\rightarrow 0$) to normal diffusion (as $t\rightarrow \infty$). Firstly,…
Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral…
We review a semi-classical transport theory for non-Abelian plasmas based on a classical picture of coloured point particles. Within this formalism, kinetic equations for the mean particle distribution, the mean fields and their…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
Despite the development of an extensive toolbox of multi-scale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatio-temporal scales. Our study offers a novel…
Near-term large quantum computers are not able to operate as a single processing unit. It is therefore required to partition a quantum circuit into smaller parts, and then each part is executed on a small unit. This approach is known as…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
In the context of NISQ computers - Noise Intermediate Scale Quantum, it is a consensus that the distribution of circuits among processing agents is a viable approach to get greater scalability with small machines. This approach can increase…
In this paper, we study a time discrete scheme for the initial value problem of the ES-BGK kinetic equation. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free…
A well-balanced scheme for a gravitational hydrodynamic system is defined as a scheme which could precisely preserve a hydrostatic isothermal solution. In this paper, we will construct a well-balanced gas-kinetic symplecticity-preserving…
In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic…
The accurate simulation of real--time quantum transport is notoriously difficult, requiring a consistent scheme to treat incoming and outgoing fluxes at the boundary of an open system. We demonstrate a method to converge non--equilibrium…
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…
The mixing of scalar substances in fluid flows by stirring and diffusion is ubiquitous in natural flows, chemical engineering, and microfluidic drug delivery. Here, we present a spectral quantum algorithm for scalar mixing by solving the…
In this paper, we demonstrate the efficiency of using semi-Lagrangian discontinuous Galerkin methods to solve the drift-kinetic equation using graphic processing units (GPUs). In this setting we propose a second order splitting scheme and a…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
From Liouville's equation, a phase-space multi-scale transport equation is systematically derived. The proposed phase-space multi-scale transport equation based on the first principle indicates that the nonlinear stochastic transport is due…