- Code Overview
- 1D Tests
- Shock Tube
- Linear Waves
- Sound Waves

- 2D Tests

This is a very simple test problem which demonstrates the accurate shock-capturing of the code. This is important, since extremely strong shocks are expected in the code's main applications. The other nice thing about this test problem is it's a relatively simple set-up and therefore an easy first test for a code intended to solve Euler's equations in spherical coordinates. There is no analytic solution, so we provide a high-resolution result that can be used to test any code.

The set-up:

if

otherwise,

We show the solution in the figure at time

An isentropic wave can be used to easily test the convergence of any code. Any smooth isentropic initial conditions will remain isentropic as long as no shocks form. For this problem, we set up a spherical pulse which expands radially outward:

In our case, we use the adiabatic index

For some reason we chose an adiabatic index

We start with a gaussian bomb designed to have total energy and mass

We allow this solution to expand over about six orders of magnitude (until

where we have defined:

Using conservation of energy we can calculate

We empirically determine for this problem

if

Otherwise, density is set to

We initiate the BMK solution at time