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Density-based schemes employing time-marching procedures available
in CFD-FASTRAN provide excellent stability and convergence characteristics for
high-speed compressible flows (typically M >0.5). However, in the low Mach
number regime (fluid velocity much smaller compared to acoustic speeds), the
convergence rates of time-marching schemes deteriorate. This user tip discusses
new features available in CFD-FASTRAN to ensure good convergence rates for both
steady and unsteady simulations at low Mach numbers.
Preconditioning is a way to accelerate convergence towards
a steady state solution by scaling the disparate eigenvalues of a system to the
same order of magnitude. The preconditioning matrix applied in CFD-FASTRAN is
chosen in such a way to provide an efficient solution for both incompressible (through
artificial compressibility) and low Mach flows (through pseudo-acoustic speeds).
Users
may select the preconditioning formulation at the ‘Advanced’ tab under ‘Solver
Conditions’ as shown in Figure 1.
Figure1. Low
Mach Preconditioning Option in CFD-FASTRAN
A simple demonstration of this feature could be found in our
model library here.
Since the preconditioning matrix is a pre-multiplier to the
time-derivative, physical time accuracy is lost. To allow time-accurate
unsteady simulations, a dual time-stepping scheme is also implemented. The flow
field at each physical time step goes through an inner pseudo-time loop where
preconditioning is applied, keeping the solutions accurate at the physical
time-step level. For unsteady simulations, with low Mach preconditioning, dual
time-stepping is automatically selected as shown in Figure 2. This feature can
also be employed for general time-dependent problems either to achieve higher
time accuracy or to take larger physical time steps while ensuring convergence
at each time step.
Figure 2. Dual Time-Stepping for
Unsteady Problems in CFD-FASTRAN
Please visit our CFD
MODEL LIBRARY often to check out more tutorials, demos and validation
cases.
If you have any questions about this feature or would like
us to discuss some other topic in the future, please let us know.
Regards,
Abraham Meganathan
ESI CFD Support Team
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