On Forward-in-Time Differencing for Fluids: Stopping Criteria for Iterative Solutions of Anelastic Pressure Equations

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Abstract
In this note, the authors address the practical issue of selecting appropriate stopping criteria for iterative solutions to the elliptic pressure equation arising in nonoscillatory, forward-in-time Eulerian and semi-Lagrangian anelastic fluid models. Using the simple computational example of 2D thermal convection in a neutrally stratified Boussinesq fluid, it is shown that (a) converging to the machine precision is not necessary for the overall accuracy and stability of the model, and adversely affects the overall model efficiency; and (b) the semi-Lagrangian model algorithm admits fairly liberal stopping criteria compared to the Eulerian flux-form model, unless the latter is formulated in terms of field perturbations. Abstract In this note, the authors address the practical issue of selecting appropriate stopping criteria for iterative solutions to the elliptic pressure equation arising in nonoscillatory, forward-in-time Eulerian and semi-Lagrangian anelastic fluid models. Using the simple computational example of 2D thermal convection in a neutrally stratified Boussinesq fluid, it is shown that (a) converging to the machine precision is not necessary for the overall accuracy and stability of the model, and adversely affects the overall model efficiency; and (b) the semi-Lagrangian model algorithm admits fairly liberal stopping criteria compared to the Eulerian flux-form model, unless the latter is formulated in terms of field perturbations.

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