FEMTC 2022

The Pressure Poisson Equation In FDS - Separable Versus Inseparable Formulation

Susanne Kilian - hhpberlin


An important design decision in FDS is the use of a simplified, so-called separable formulation of the Poisson equation for the pressure, which entails a considerable saving in computational effort compared to the full, inseparable formulation. 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 still not be captured quickly enough in time.

In such cases, it can be appropriate to actually use the full density-dependent pressure system 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 powerful than the FFT. Overall, a good balance must be found between the higher accuracy of inseparable approach and the higher performance of separable approach.

First concepts for using the inseparable Poisson system have already been integrated into the alternative pressure solver ScaRC and validated on various test cases. The presentation explains the above background and shows the current state of development including various comparative calculations to the separable approach.

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