Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations

TL;DR

This paper derives a family of exact solutions for 2D axisymmetric inviscid compressible flows, useful for code verification and modeling, based on assumptions of separable velocity fields and specific physical constraints.

Contribution

It introduces a new class of exact, analytically derived solutions for 2D axisymmetric compressible flows under ideal gas conditions, expanding the toolkit for verification and modeling.

Findings

Derived infinite family of solutions including elliptic and hyperbolic types

Solutions depend on nonlinear ODE systems and physical constraints

Discussed applications in code verification and model qualification

Abstract

We investigate the two-dimensional ($2$D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the $2$D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an infinite family of elliptic or hyperbolic, uniformly expanding or contracting ``gas cloud'' solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.