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This paper presents an accurate and robust fourth order gas-kinetic scheme on two dimensional unstructured hybrid mesh for incompressible and compressible viscous flows. For generalized Riemann problem and Navier-Stokes solution, the…

Fluid Dynamics · Physics 2017-11-22 Dongxin Pan , Chengwen Zhong , Congshan Zhuo

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Following the direct modeling methodology of the unified…

Computational Physics · Physics 2020-10-28 Yipei Chen , Yajun Zhu , Kun Xu

The rarefied flow and multi-scale flow are crucial for the aerodynamic design of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete velocity space, the Boltzmann method, such as the discrete velocity method and…

Fluid Dynamics · Physics 2025-04-07 Jianfeng Chen , Sha Liu , Rui Zhang , Chengwen Zhong , Yanguang Yang , Congshan Zhuo

Improving the efficiency of the direct simulation Monte Carlo (DSMC) method has become increasingly urgent with the rapid development of space exploration. To address this issue, the direct intermittent general synthetic iteration (DIG)…

Computational Physics · Physics 2025-11-25 Bin Hu , Liyan Luo , Kaiyuan Wang , Lei Wu

In this paper, a third-order compact gas-kinetic scheme is firstly proposed for three-dimensional computation for the compressible Euler and Navier-Stokes solutions. The scheme achieves its compactness due to the time-dependent gas…

Computational Physics · Physics 2020-09-08 Xing Ji , Fengxiang Zhao , Wei Shyy , Kun Xu

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…

Numerical Analysis · Mathematics 2017-08-15 Benjamin Krank , Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

We introduce numerical solvers for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. Due to the quadratic collision operator in the Boltzmann equation, the SGS method requires solving a nonlinear system…

Computational Physics · Physics 2023-11-27 Tianai Yin , Zhenning Cai , Yanli Wang

This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard…

Computational Physics · Physics 2017-10-05 Salli Moustafa , François Févotte , Mathieu Faverge , Laurent Plagne , Pierre Ramet

This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…

Fluid Dynamics · Physics 2026-04-17 Hangkong Wu , Yuze Zhu , Yajun Zhu , Kun Xu

The impressive progress of the kinetic schemes in the solution of gas dynamics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods…

Plasma Physics · Physics 2013-05-06 B. Chetverushkin , N. D'Ascenzo , V. Saveliev

The performance of high-order gas-kinetic scheme (HGKS) has been investigated for the direct numerical simulation (DNS) of isotropic compressible turbulence up to the supersonic regime. Due to the multi-scale nature and coupled…

Computational Physics · Physics 2020-05-19 Guiyu Cao , Liang Pan , Kun Xu

We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic…

Computational Physics · Physics 2015-07-23 Sergey Zabelok , Robert Arslanbekov , Vladimir Kolobov

Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the…

Fluid Dynamics · Physics 2022-07-20 W. Liu , Z. J. Liu , Z. L. Zhang , C. J. Teo , C. Shu

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…

Numerical Analysis · Mathematics 2024-03-04 Yaqing Yang , Liang Pan , Kun Xu

An efficient algorithm for computing the terms appearing in the Generalised Kolmogorov Equation (GKE) written for the indefinite plane channel flow is presented. The algorithm, which features three distinct strategies for parallel…

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…

The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic…

Computational Physics · Physics 2021-02-03 Xiaocong Xu , Yipei Chen , Kun Xu

Large scale, inverse problem solving deep learning algorithms have become an essential part of modern research and industrial applications. The complexity of the underlying inverse problem often poses challenges to the algorithm and…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-07-02 Daniel Lersch , Malachi Schram , Zhenyu Dai , Kishansingh Rajput , Xingfu Wu , N. Sato , J. Taylor Childers

We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…

Optimization and Control · Mathematics 2022-09-13 Wicak Ananduta , Sergio Grammatico

For the one-stage third-order gas-kinetic scheme (GKS), success applications have been achieved for the three-dimensional compressible flow computations [33]. The high-order accuracy of the scheme is obtained directly by integrating a…

Numerical Analysis · Mathematics 2019-02-20 Liang Pan , Kun Xu