Stability Analysis of Quadrature-Based Moment Methods for Kinetic Equations

Convergence of moment methods for linear kinetic equations

Numerical methods for linear kinetic equations based on moment expansions for a discretization in the velocity direction are examined. The moment equations are hyperbolic systems which can be shown to converge to the kinetic equation as the order of the expansion tends to innnity and to a drift-diiusion model as the Knudsen number tends to zero. A discretiza-tion of the moment equations with re...

Stability Analysis of Quadrature Methods for Two-Dimensional Singular Integral Equations

In this paper we apply a quadrature method based on the tensor product trapezoidal rule to the solution of a singular integral equation over the two-dimensional torus. We prove that this method is stable if and only if a certain numerical symbol does not vanish. For a special kernel function, we present a plot of numerically computed symbol values and, for symmetric kernels (Mikhlin-Giraud kern...

Realizable high-order finite-volume schemes for quadrature-based moment methods applied to diffusion population balance equations

Dilute gas–particle flows can be described by a kinetic equation containing terms for spatial transport, gravity, fluid drag and particle–particle collisions. However, direct numerical solution of kinetic equations is often infeasible because of the large number of independent variables. An alternative is to reformulate the problem in terms of the moments of the velocity distribution. Recently,...

Scalable Methods for Kinetic Equations

Scalable Methods for Kinetic Equations