Fundamental Algorithms in Computational Fluid Dynamics by Thomas H. Pulliam & David W. Zingg

Author:Thomas H. Pulliam & David W. Zingg
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.66)

where is a user defined constant. This operator is sufficient to damp unwanted high-frequency modes and provide stability while generally adding an error that is smaller than the second-order error associated with the centered difference scheme. However, it is not sufficient to prevent oscillations at discontinuities. For this purpose, the following first-order symmetric operator is typically used:

(4.67)

The artificial dissipation scheme used in the implicit finite-difference algorithm of this chapter combines the above two operators using a pressure sensor to detect shock waves [6, 12]. This approach is intended for flows with shock waves, where the pressure is discontinuous; it will not sense a discontinuity such as a contact surface across which the pressure is continuous. Before presenting the operator, we note that

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