A CFD Application

In this section we discuss another significant HPJava application code. This code solves the Euler equations for inviscid fluid flow by a finite volume approach. One version of this code, viewable at http://www.hpjava.org/demo.html also has a novel parallel GUI implemented in HPJava.

The Euler equations are a family of conservation equations, relating the time rates of change of various densities to divergences of associated flow fields. In two dimensions there are four densities--the ordinary matter density, densities of the two components of momentum, and the energy density. The Euler equations can be summarized as a conservation equation for four-component vectors $U$, $f$ and $g$:

$$\frac{\partial U}{\partial t} + \frac{\partial f}{\partial x} + \frac{\partial g}{\partial y} = 0$$ (1)

The flow variables $(f, g)$ are related to the dependent variables $U$ by simple (but non-linear) algebraic equations. So the set of differential equations is closed. Two important quantities that figure in the equations are the pressure, $p$, and the enthalpy per unit mass, $H$, which can be computed from the components of $U$ using the equations of state for the fluid.