Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

Liu, Chang; Xu, Kun

doi:10.1186/s42774-021-00062-1

Cited by 25 publications

(6 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The discrete conservation law in a control volume j is, where W(x, t) is the conservative flow variable in a control volume j , and F(t) is the corresponding flux across the cell interface ∂� j . The above integral conservation law is valid in any flow regimes from the rarefied to the continuum one once the dynamics of F(t) can be properly modeled [25,26]. The accuracy of the updated solution depends…”

Section: Solution Updatesmentioning

confidence: 99%

High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

Zhao

Shyy

et al. 2023

Adv. Aerodyn.

Self Cite

View full text Add to dashboard Cite

A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of flow variables construct a time-accurate evolution solution of gas distribution function at a cell interface and obtain the corresponding flux function; 2). Introduce the WENO-type weighting functions into the high-order time-derivative of the cell interface flux function in the multistage multi-derivative (MSMD) time stepping scheme to cope with the possible impingement of a shock wave on a cell interface within a time step, and update the cell-averaged conservative flow variables inside each control volume; 3). Model the time evolution of the gas distribution function on both sides of a cell interface separately, take moments of the inner cell interface gas distribution function to get flow variables, and update the cell-averaged gradients of flow variables inside each control volume; 4). Based on the cell-averaged flow variables and their gradients, develop compact initial data reconstruction to get initial condition of flow distributions at the beginning of next time step. A compact gas-kinetic scheme (GKS) up to sixth-order accuracy in space and fourth-order in time has been constructed on 2D unstructured mesh. In this paper, the compact GKS up to fourth-order accuracy on three-dimensional tetrahedral mesh will be further constructed with the focus on the WENO-type initial compact data reconstruction. Nonlinear weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock interactions. The fourth-order compact GKS uses a large time step with a CFL number 0.6 in the simulations from subsonic to hypersonic flow. A series of test cases are used to validate the scheme. The high-order compact GKS can be used in 3D applications with complex geometry.

show abstract

Section: Solution Updatesmentioning

confidence: 99%

High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

Zhao

Shyy

et al. 2023

Adv. Aerodyn.

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the Orszag-Tang vortex problem, the initial condition is as follows, and we refer [21,25] for more details.…”

Section: Orszag-tang Vortexmentioning

confidence: 99%

“…Moreover, the energy-conserving implicit PIC algorithms for the VM system with a finite difference method in the physical space are proposed in [27], while a fully implicit solver for the VA system based on Newton-Krylov methods is proposed in [8]. Recently, a highly efficient UGKWP method, combined with the deterministic UGKS method and the stochastic Monte Carlo method, has been proposed to solve the Boltzmann equations and then extended to the VM system [25].…”

Section: Introductionmentioning

confidence: 99%

Highly efficient energy-conserving moment method for the multi-dimensional Vlasov-Maxwell system

Yin¹,

Zhong²,

Wang³

2022

Preprint

View full text Add to dashboard Cite

In this paper, we propose an energy-conserving numerical method to solve the Vlasov-Maxwell (VM) system based on the regularized moment method proposed in [4]. The globally hyperbolic moment system is deduced for the multi-dimensional VM system under the framework of the Hermite expansions, where the expansion center and the scaling factor are set as the macroscopic velocity and local temperature, respectively. Thus, the effect of the Lorentz force term can be reduced into several ODEs about the macroscopic velocity and the moment coefficients of higher order, which could significantly reduce the computational cost of the whole system. An energy-conserving numerical scheme is proposed to solve the moment equations and Maxwell's equations, where only a linear equation system needs to be solved. Several numerical examples such as the two-stream instability, Weibel instability, and the two-dimensional Orszag-Tang vortex problem are studied to validate the efficiency and excellent energy-preserving property of the numerical scheme.

show abstract

“…The UGKS couples transport and collision processes using a multiscale flux function obtained from the integral solution of the kinetic model equation. Initially developed in the rarefied gas dynamics [46], the UGKS has been applied to a wide range of transport processes [21,22], including photon transport [37,39]. Other approaches have also been developed to speed up convergence for iteration schemes in the field of rarefied gas dynamics, such as the general synthetic iterative scheme (GSIS) [43,36] and the discrete unified gas-kinetic scheme (DUGKS) [7,6].…”

Section: Introductionmentioning

confidence: 99%

Unified Gas-Kinetic Particle Method for Frequency-dependent Radiation Transport

Li¹,

Liu²,

Song³

2023

Preprint

View full text Add to dashboard Cite

This paper proposes a unified gas-kinetic particle (UGKP) method for the frequency-dependent photon transport process. The photon transport is a typical multiscale process governed by the nonlinear radiative transfer equations (RTE). The flow regime of photon transport varies from the ballistic regime to the diffusive regime with respect to optical depth and photon frequency. The UGKP method is an asymptotic preserving (AP) scheme and a regime adaptive scheme. The teleportation error is significantly reduced, and the computational efficiency is remarkably improved in the diffusive regime. Distinguished from the standard multigroup treatment, the proposed UGKP method solves the frequency space in a non-discretized way. Therefore the Rosseland diffusion system can be precisely preserved in the optically thick regime. Taking advantage of the local integral solution of RTE, the distribution of the emitted photon can be constructed from its macroscopic moments. The Monte Carlo particles in the UGKP method need only be tracked before their first collision events, and a re-sampling process is performed to close the photon distribution for each time step. The large computational cost of excessive scattering events can be saved, especially in the optically thick regime. The proposed UGKP method is implicit and removes the light speed constraint on the time step. The particle tracking approach combining the implicit formulation makes the proposed UGKP method an efficient solution algorithm for frequency-dependent radiative transfer problems. We demonstrate with numerical examples the capability of the proposed multi-frequency UGKP method.

show abstract

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

Cited by 25 publications

References 46 publications

High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

Highly efficient energy-conserving moment method for the multi-dimensional Vlasov-Maxwell system

Unified Gas-Kinetic Particle Method for Frequency-dependent Radiation Transport

Contact Info

Product

Resources

About