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1 results

  • 7 - Compressible Flow and Rapid Prototyping

  • from Part II - Single-Phase Flow
  • Knut-Andreas Lie
  • Book:
    An Introduction to Reservoir Simulation Using MATLAB/GNU Octave
    Published online:
    22 July 2019
    Print publication:
    08 August 2019, pp 202-228
    • Chapter
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  • 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.