A Variational Approach to Monte Carlo Renormalization Group

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The 2D Ising model is used to illustrate the method.Comment: 4 pages, 3 figures, 1 tabl

Accuracy, Scalability, and Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

The unstructured, mixed-element, cell-centered, finite-volume flow solver USM3D is enhanced with new capabilities including parallelization, line generation for general unstructured grids, improved discretization scheme, and optimized iterative solver. The paper reports on the new developments to the flow solver and assesses the accuracy, scalability, and efficiency. The USM3D assessments are conducted using a baseline method and the recent hierarchical adaptive nonlinear iteration method framework. Two benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere-cylinder configuration and a transonic flow around the ONERA M6 wing are considered

Time integration for diffuse interface models for two-phase flow

We propose a variant of the $\theta$-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional stabilizing force terms, or a fully implicit coupling of the Navier-Stokes and Cahn-Hilliard equation. In the common case that the equations for interface and flow are coupled explicitly, we find a time step restriction which is very different to other two-phase flow models and in particular is independent of the grid size. We also show that the proposed stabilization techniques can lift this time step restriction. Even more pronounced is the performance of the proposed fully implicit scheme which is stable for arbitrarily large time steps. We demonstrate in a Taylor flow application that this superior coupling between flow and interface equation can render diffuse interface models even computationally cheaper and faster than sharp interface models