euler

Last Updated: 30 August 2023

A 2-D Euler solver for internal flows written in Fortran.

Background

This code solves the 2-D Euler equations,

$\frac{\partial q}{\partial t} + \frac{\partial f}{\partial x} + \frac{\partial g}{\partial y} = 0,$

where the state and flux vectors are written in conservative variable form, i.e.

$$q = \begin{Bmatrix} \rho \\ \rho u \\ \rho v \\ \rho E \end{Bmatrix}, \quad f = \begin{Bmatrix} \rho u \\ \rho u^2 + p \\ \rho uv \\ \rho Hu \end{Bmatrix}, \quad\text{and}\quad g = \begin{Bmatrix} \rho \\ \rho uv \\ \rho v^2 + p \\ \rho Hv \end{Bmatrix}.$$

Features

Models both subsonic and supersonic flow; however, supersonic inlet conditions are not yet supported (see roadmap).

Both an algebraic and elliptic grid generation algorithm are included - therefore only structured grids are supported.

Example Simulation

A channel flow simulated using:

• $(i_\text{max}, j_\text{max}) = (201, 41)$
• $M_\infty = 0.7$
• $\nu_2 = 0.3$
• $\nu_4 = 0.003$
• $p_\text{exit} = 0.8\cdot{}p_\infty$
• $\alpha = 0$
• $\varepsilon = 1\times10^{-8}$
• $\text{CFL} = 1$

Solution:

Residual:

Force:

Roadmap

• verify that the code works for mach 0.3, 0.5, 0.7
• verify grid independence of solutions
• implement force calculations across bottom of the domain
• add support for supersonic inlet conditions
• extend support for different domains (i.e. nozzles)
• add support for Tecplot videos
• add support for other plotting software (since Tecplot is paywalled)
• couple with method of characteristics design tool