Related papers: Fast-Converging and Asymptotic-Preserving DSMC
We consider a Lattice Boltzmann type discrete velocity model in the low Mach number scaling and develop a corresponding numerical scheme that remains uniformly valid across all regimes of the mean free path, from the kinetic to the…
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…
Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations…
We present a study of single-mode Rayleigh-Taylor instabilities (smRTI) with a modified Direct Simulation Monte Carlo (mDSMC) code in two dimensions. The mDSMC code is aimed to capture the dynamics of matter for a large range of Knudsen…
The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…
This paper enhances the Diffuse Interface Method (DIM) for simulating compressible multiphase flows across all Mach numbers by addressing the accuracy challenges posed at low Mach regimes. A correction to the Riemann solver is introduced,…
Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional…
The discontinuous Galerkin (DG) method is widely being used to solve hyperbolic partial differential equations (PDEs) due to its ability to provide high-order accurate solutions in complex geometries, capture discontinuities, and exhibit…
We present a Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous multispecies Landau-Fokker-Planck equation. The scheme is derived from a first-order approximation of the multispecies Boltzmann operator in the grazing…
It has recently been demonstrated that dynamical low-rank algorithms can provide robust and efficient approximation to a range of kinetic equations. This is true especially if the solution is close to some asymptotic limit where it is known…
We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
In plasma edge simulations, kinetic Monte Carlo (MC) is often used to simulate neutral particles and estimate source terms. For large-sized reactors, like ITER and DEMO, high particle collision rates lead to a substantial computational cost…
The parallel solver of the general synthetic iterative scheme (GSIS), as recently developed by Zhang \textit{et. al.} in Comput. Fluids 281 (2024) 106374, is an efficient method to find the solution of the Boltzmann equation…
We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collision…
In rarefied gas flows, the spatial grid size could vary by several orders of magnitude in a single flow configuration (e.g., inside the Knudsen layer it is at the order of mean free path of gas molecules, while in the bulk region it is at a…
Oscillatory rarefied gas flows are frequently encountered in MEMS, and their efficient numerical simulation remains a major challenge due to the time dependent nature of the problem and the high dimensionality of the Boltzmann kinetic…
In the spirit of making high-order discontinuous Galerkin (DG) methods more competitive, researchers have developed the hybridized DG methods, a class of discontinuous Galerkin methods that generalizes the Hybridizable DG (HDG), the…
We present a Discontinuous Galerkin (DG) solver for the compressible Navier-Stokes system, designed for applications of technological and industrial interest in the subsonic region. More precisely, this work aims to exploit the…
We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck…