The Pressure Poisson Equation In FDS - Simplified Versus Complete Formulation

An important design decision in FDS is the use of a simplified version of the pressure Poisson equation, which results in a significant saving in computational effort compared to the complete version. The underlying simplification strategy is based on eliminating the dependence on continuously varying density terms from the associated system matrix, which would otherwise have to be rebuilt twice at each individual time step with correspondingly high cost. Instead, a highly structured matrix with constant entries is obtained, which can essentially be used over the entire simulation course and allows the mesh-wise application of highly optimized and extremely fast FFT methods.

A possible disadvantage of this simplification is that current density changes enter the individual systems of equations only with a delay of one time step. For typical building fires, this issue is generally not a problem, but for very long tunnel geometries numerical instabilities may occur. Although an additional iterative correction procedure is applied within each pressure solution to compensate for this delay, turbulent dynamics (i.e. large oscillations in the mass flow) may not be captured quickly enough.

In such cases, it can be appropriate to actually use the complete density-dependent pressure equation instead. However, apart from the very frequent matrix reconstruction involved, another drawback of this strategy is that more robust solvers must be used for the resulting variable matrices, which unfortunately are much less performant than the FFT. Overall, a good balance must be found between the higher accuracy of the complete formulation and the higher performance of simplified one.

First concepts for using the complete pressure Poisson equation have already been integrated into the alternative pressure solver UScaRC and validated on various test cases. With regard to the very challenging tunnel use cases, the presentation explains the upper background, shows the current state of development as well as another helpful feature, namely the tunnel preconditioner.