7 - Compressible Flow and Rapid Prototyping

Summary

This chapter explains how you can discretize the basic equations for single-phase, compressible flow by use of the discrete differential and averaging operators introduced in Chapter 4. These operators enable you to implement the flow equations in a compact form similar to the continuous mathematical description. By using automatic differentiation, you can automatically linearize and assemble the corresponding linear system without having to explicitly derive and implement expressions for partial derivatives in the Jacobian matrix. The combination of discrete operators and automatic differentiation with a flexible grid structure, a highly vectorized and interactive scripting language, and a powerful graphical environment, is the main reason MRST has proven to be an efficient tool for developing new proof-of-concept codes. To demonstrate this, we first develop a compact solver for compressible flow, and then extend the basic single-phase model to include pressure-dependent viscosity, non-Newton fluid behavior, and temperature effects.