Article
Computer Science, Interdisciplinary Applications
Shi Jin, Min Tang, Xiaojiang Zhang
Summary: This paper presents a scheme with asymptotic preserving (AP) properties in both space and time for the radiation magnetohydrodynamics (RMHD) system. By decomposing the radiative intensity into three parts and utilizing suitable combinations of explicit and implicit discretizations, the stability condition and computational efficiency are guaranteed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Bert Mortier, Martine Baelmans, Giovanni Samaey
Summary: We propose a novel Monte Carlo strategy for simulating the BoltzmannBGK model in the presence of both low-collisional and high-collisional regimes. Our method uses hybridized particles that exhibit both kinetic and diffusive behavior depending on the local collisionality, ensuring accuracy in low-collisional regimes and removing exploding simulation costs in high-collisional regimes.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Bert Mortier, Pieterjan Robbe, Martine Baelmans, Giovanni Samaey
Summary: We have developed a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation. By incorporating this method within a Multilevel Monte Carlo (MLMC) framework and utilizing a hierarchy of larger time step sizes, the simulation cost is further reduced. The ML-KDMC method outperforms the single-level KDMC method by several orders of magnitude, demonstrating its efficiency.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
K. R. Arun, A. J. Das Gupta, S. Samantaray
Summary: This paper presents an analysis of an asymptotic preserving (AP) IMEX-RK finite volume scheme for the wave equation system in the zero Mach number limit. The scheme demonstrates uniform second order convergence with respect to the Mach number and maintains accuracy and stability properties for both time semi-discrete and space-time fully-discrete schemes. Extensive numerical case studies confirm the effectiveness of the scheme.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Min Tang, Li Wang, Xiaojiang Zhang
Summary: The translation discusses an asymptotic preserving scheme for the gray radiative transfer equation, introducing an auxiliary variable to solve an implicit nonlinear system and using a three-stage update. The method preserves accurate simulation results in both the nonlinear diffusion limit and the free streaming limit.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Physics, Mathematical
Jinjing Xu, Fei Zhao, Zhiqiang Sheng, Guangwei Yuan
Summary: In this paper, a new nonlinear cell-centered finite volume scheme is proposed for two dimensional anisotropic diffusion problems on general polygonal meshes, which preserves discrete maximum principle (DMP). The scheme achieves second-order accuracy, maintains maximum and minimum values for solutions, and is conservative.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Xiaojiang Zhang, Peng Song, Yi Shi, Min Tang
Summary: This paper proposes a new decomposed multi-group method for frequency discretization that achieves full frequency adaptivity in both gray radiation diffusion and frequency-dependent diffusion limits. The method allows for tuning the frequency discretization of the limiting models and has been verified through numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Luis Almeida, Benoit Perthame, Xinran Ruan
Summary: The study introduces an asymptotic preserving (A-P) scheme for a population model structured by age and a phenotypical trait, demonstrating the accuracy and numerical resolution capability of the scheme. The scheme exhibits the A-P property and is applicable even in cases with mutations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mechanics
Xuyao Yuan, Wei Wei, Zhenlong Fang, Yong Chen
Summary: In this work, a simple, stable, and purely local pressure-based double-population lattice Boltzmann model is proposed for low-Mach number variable-density flow. The model recovers the continuity, momentum, and energy equations describing the flow and accurately predicts the drag coefficient and Nusselt number for different Reynolds numbers.
Article
Computer Science, Interdisciplinary Applications
Lukas Einkemmer, Jingwei Hu, Yubo Wang
Summary: The proposed method reduces the computational complexity of solving the multi-scale multi-dimensional linear transport equation through macro-micro decomposition and low-rank approximation, achieving second-order accuracy and asymptotic-preserving property. It demonstrates high efficiency in handling different regimes and can be implemented in a fully explicit way.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Florian Blachere, Christophe Chalons, Rodolphe Turpault
Summary: This paper focuses on the numerical approximation of hyperbolic systems of conservation laws with stiff source terms and parabolic degeneracy in the asymptotic limit. The approach involves a simple modification of the numerical flux associated with the usual HLL scheme to control numerical diffusion, allowing for capturing correct asymptotic behavior and preserving high-order accuracy in the asymptotic limit. Numerical experiments are conducted to illustrate these properties.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Yupeng Ren, Yulong Xing, Dean Wang, Jianxian Qiu
Summary: In this paper, the combination of HWENO scheme and FSM method is proposed for solving the steady-state S-N transport equation in the finite volume framework. The asymptotic preserving property of the high order finite volume HWENO method is demonstrated, and a hybrid strategy is introduced to compute the nonlinear weights in the HWENO reconstruction for computational efficiency improvement.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Physics, Fluids & Plasmas
N. G. Kallikounis, B. Dorschner, I. Karlin
Summary: A multi-scale lattice Boltzmann scheme is proposed to adaptively refine particles' velocity space, efficiently coupling different velocity sets of lower and higher order. The scheme shows flexibility in model selection and reduction in computational requirements, validated in various flow setups.
Article
Physics, Mathematical
Patricia Goncalves, Kohei Hayashi
Summary: This paper investigates a microscopic model of interacting oscillators with two conserved quantities, volume, and energy. The system is driven by a general nonlinear potential under high-temperature regime, where the inverse temperature of the system is taken to be asymptotically small. It is shown that the fluctuations of one field converge to the solution of an additive stochastic heat equation or the stochastic Burgers equation depending on the asymmetric regime, while the fluctuations of the other field cross from an additive stochastic heat equation to a fractional diffusion equation given by a skewed Levy process.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Jinjing Xu, Fei Zhao, Zhiqiang Sheng, Guangwei Yuan
Summary: In this paper, the neutron diffusion kinetics equation with delayed neutrons is studied. A positivity theorem is proposed, and a nonlinear positivity-preserving finite volume scheme is developed to deal with discontinuous and anisotropy diffusion coefficient problems. The existence of solution for the nonlinear system is proved under certain constraint on time step size. Three nonlinear iteration strategies are introduced to solve the system. Numerical experiments demonstrate the scheme's positivity-preserving property and second order accuracy in space. The computational costs of the iteration strategies are compared, and a necessary constraint on time step size for convergence is shown with another example.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)