Consistency Stability, Convergence Of Stirling Engine Models

Stirling engine modeling can be divided into two main steps. First, an idealization of the engine that can be translated Into a complete and unique mathematical problem must be chosen. Then, a computer code that provides a numerical, approximate solution to that problem must be written. The solution Is meaningful If the error due to Its approximate nature can be made arbitrarily small by dividing the machine into an increasingly larger number of smaller volumes and time into an Increasingly larger number of smaller Intervals. In the limit the solution becomes independent of the numerical parameters. The first step is thus to select a cost-offective idealization for the engine. A one-dimensional model, neglecting inertia of the fluid, is a reasonable compromise. However, the numerical solution of that problem Is not straightforward because the solution to the Idealized problem has discontinuities when flow reverse] occurs near abrupt changes of cross-section, and those discontinuities do not die instantly. Numerical schemes that are practical and able to deal with discontinuities are relatively inaccurate for coarse mesh sizes. For accurate results, a particularly fine discretization of time and space Is required. The opu time required is nevertheless affordable if the code is fully vectorized on a supercomputer.