Related papers: High order semi-Lagrangian methods for the BGK equ…
This paper focuses on a nonlinear convection-diffusion equation with space and time-fractional Laplacian operators of orders $1<\beta<2$ and $0<\alpha\leq1$, respectively. We develop local discontinuous Galerkin methods, including Legendre…
Based on the Hermite expansion of the distribution function, we introduce a Galerkin spectral method for the spatially homogeneous Boltzmann equation with the realistic inverse-power-law models. A practical algorithm is proposed to evaluate…
Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular…
A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on an extended equilibrium state that is constructed to reproduce the…
Based on the recent development of Jacobian-free Lax-Wendroff (LW) approaches for solving hyperbolic conservation laws [Zorio, Baeza and Mulet, Journal of Scientific Computing 71:246-273, 2017], [Carrillo and Par\'es, Journal of Scientific…
In this work we consider the classical non-linear Boltzmann equation, where the unknown is the distribution function $f$, which depends on the time $t$, the vector $\mathbf{x}$ (the position of a molecule) and its velocity $\mathbf{\xi}$.…
In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge-Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems,…
In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a low rank numerical method is proposed to correct the modeling…
We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier-Stokes equations resulting from combining an $H(\mathrm{div}, \Omega)$-conforming discontinuous Galerkin spatial discretization, and…
We present a new high-order accurate Lagrangian discontinuous Galerkin (DG) hydrodynamic method to simulate material dynamics (for e.g., gasses, fluids, and solids) with up to fourth-order accuracy on cubic meshes. The variables, such as…
The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…
We present a numerical method for simulating rarefied gases that interact with moving boundaries and rigid bodies. The gas is described by the BGK equation in Lagrangian form and solved using an Arbitrary Lagrangian-Eulerian method, in…
The aim of this paper is to apply a high-order discontinuous-in-time scheme to second-order hyperbolic partial differential equations (PDEs). We first discretize the PDEs in time while keeping the spatial differential operators…
A recently introduced family of lattice Boltzmann (LB) models (Karlin, B\"osch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for incompressible two-dimensional flows. A framework for developing LB models based on entropy…
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…
Due to limited possibilities of experimental investigations for non-equilibrium gas flows, numerical results are of highest interest. Although the well-established Direct Simulation Monte Carlo (DSMC) method achieves highly accurate…
A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…
Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous Galerkin (LDG) method for the distributed-order time and…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the…