Convergence of a Particle Method for Diffusive Gradient Flows in One Dimension

A diffusive information preservation method for small Knudsen number flows

Keywords: DSMC IP Molecular diffusion Time step Cell size a b s t r a c t The direct simulation Monte Carlo (DSMC) method is a powerful particle-based method for modeling gas flows. It works well for relatively large Knudsen (Kn) numbers, typically larger than 0.01, but quickly becomes computationally intensive as Kn decreases due to its time step and cell size limitations. An alternative appro...

A Vortex Particle Method for Compressible Flows

A vortex particle method for the simulation of twodimensional compressible flows is developed. The computational elements are Lagrangian particles that carry vorticity, dilatation, enthalpy, entropy and density. The velocity field is decomposed into irrotational and solenoidal parts, which allows its calculation in terms of the particles’ vorticity and dilatation. The particle coverage is trunc...

Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension

We study the long time behavior of the Wasserstein gradient flow for an energy functional consisting of two components: particles are attracted to a fixed profile ω by means of an interaction kernel ψa(z) = |z|a , and they repel each other by means of another kernel ψr(z) = |z|r . We focus on the case of one space dimension and assume that 1 ≤ qr ≤ qa ≤ 2. Our main result is that the flow conve...

Strong Convergence of a Projected Gradient Method

Convergence Analysis for a Nonsymmetric Galerkin Method for a Class of Singular Boundary Value Problems in One Space Dimension

For the method and problems under consideration we estimate the error in the maximum norm as well as at individual nodal points. In order to obtain full superconvergence at all nodal points we have to introduce local mesh refinements, even though the exact solution is smooth for the given class of problems.