In [16, 17], we constructed uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics with the ideal gas equation of state. The technique also applies to high order accurate finite volume schemes. For the Euler equations with various source terms (e.g., gravity and chemical reactions),...

Method: The presented EL method uses the open access software OpenFOAM to solve bubble dynamics with bubble interactions computed via Monte Carlo methods. The estimated bubble size distribution and the predicted hold-up are compared with experimental data and other simulative EE work with a reasonable consensus for both. Benchmarks with state of the art EE simulations shows that the EL approach...

This article surveys the Euler calculus — an integral calculus based on Euler characteristic — and its applications to data, sensing, networks, and imaging.

Progresses on the dynamical system theory of 2D Euler equation are reported. An open problem is presented. The isospectral theory on Lax pairs of Euler equations is initiated.

For an arbitrary ribbon graph G, the partial-dual Euler-genus polynomial of G is a generating function that enumerates partial duals by Euler genus. When orientable graph, genus Gross, Mansour, and Tucker inaugurated these distribution problems in 2020. A bouquet one-vertex graph. Given its same as some bouquet; this motivates our focus on bouquets. We obtain polynomials for all bouquets with a...