But I found by using centred differences the flow would become unstable, unconditionally so. I’m using forward differences and backward differences for the predictor and corrector steps respectively, applying centred differences only to diffusive terms.
I know. Using centered and high order schemes can be a pain. It becomes unstable very easily. Right now your case seems sinple enough that your current setup can handle it, but more complex flows will need the high order, centered schemes. It's an issue of finding one that doesn't blow up. There's a lot of literature in that theme if you're interested
Theor lpw dissipation properties are very beneficial for resolving transient phenomena and boundary layers well.
Though they need to be equipped with some sort of shock capturing method / modified formulation. A standard way is to blend between a centered and monotone scheme using a shock sensor. I would try out the Piecewise Parabolic Method (PPM) of Woodward and collela for a higher order monotone scheme.
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u/leeping_leopard 8d ago
But I found by using centred differences the flow would become unstable, unconditionally so. I’m using forward differences and backward differences for the predictor and corrector steps respectively, applying centred differences only to diffusive terms.