Related papers: THC: a new high-order finite-difference high-resol…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the…
This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm…
We compare the results of numerical simulations of thin and quasi-spherical (thick) accretion flows with existing analytical solutions. We use a Lagrangian code based on the Smooth Particle Hydrodynamics (SPH) scheme and an Eulerian finite…
A new multiple-relaxation-time lattice Boltzmann scheme for compressible flows with arbitrary specific heat ratio and Prandtl number is presented. In the new scheme, which is based on a two-dimensional 16-discrete-velocity model, the moment…
This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal discretization in [{\em J. Li and Z. Du, A…
A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented. The governing equations employ Chorin's classical artificial compressibility (AC) formulation cast in…
Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting)…
We present in this paper a computational approach based on molecular dynamics simulations and graph theory to characterize the structure of liquid water considering not only the local structural arrangement within the first (or second)…
In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO…
We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave…
Using classical as well as ab-initio molecular dynamics simulations, we calculate the frequency-dependent shear viscosity of pure water and water-glycerol mixtures. In agreement with recent experiments, we find deviations from…
We introduce a shell (``GOY'') model for turbulent binary fluids. The variation in the concentration between the two fluids acts as an active scalar leading to a redefined conservation law for the energy, which is incorporated into the…
Recent experiments have provided compelling and renewed interest in phonon hydrodynamics. At variance with ordinary diffusive heat transport, this regime is primarily governed by momentum-conserving phonon collisions. At the mesoscopic…
This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be…
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed…
In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-order hybrid fast sweeping scheme for solving steady state…
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…
Using a new numerical code we have carried out two-dimensional simulations of the nonlinear evolution of unstable sheared magnetohydrodynamic flows. We considered two cases: a strong magnetic field (Alfven Mach number, M_a = 2.5) and a weak…
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)…