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In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The p-multigrid strategy is a…
A discrete unified gas kinetic scheme (DUGKS) coupled with the immersed boundary (IB) method is developed to perform interface-resolved simulation of particle-laden flows. The present method (IB-DUGKS) preserves the respective advantages of…
Simulating nonlinear partial differential equations (PDEs) such as the Navier--Stokes (NS) equations remains computationally intensive, especially when implicit time integration is used to capture multiscale flow dynamics. This work…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
In this paper, a high-order gas-kinetic scheme in general curvilinear coordinate (HGKS-cur) is developed for the numerical simulation of compressible turbulence. Based on the coordinate transformation, the Bhatnagar-Gross-Krook (BGK)…
In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for general nonlinear convection-diffusion equation (NCDE), and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
We develop the steady-state regularized 13-moment equations in the linear regime for rarefied gas dynamics with general collision models. For small Knudsen numbers, the model is accurate up to the super-Burnett order, and the resulting…
The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the…
In this paper, a uniformly high-order discontinuous Galerkin gas kinetic scheme (DG-HGKS) is proposed to solve the Euler equations of compressible flows. The new scheme is an extension of the one-stage compact and efficient high-order GKS…
Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional…
Moment models with suitable closure can lead to accurate and computationally efficient solvers for particle transport. Hence, we propose a new asymptotic preserving scheme for the M1 model of linear transport that works uniformly for any…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
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…
The kinetic Boltzmann equation models gas dynamics over a wide range of spatial and temporal scales. Simplified versions of the full Boltzmann collision operator, such as the classical Bhatnagar-Gross-Krook and the closely related…
This work discusses the performance of a modern numerical scheme for fluid dynamical problems on modern high-performance computing architectures. Our code implements a spatial nodal discontinuous Galerkin scheme that we test up to an order…
We propose a systematic methodology to derive the regularized thirteen-moment equations in the rarefied gas dynamics for a general class of linearized collision models. Detailed expressions of the moment equations are written down for all…
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian…
In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…