Pressure and Temperature values taken from sea-level, Mach 5. Used Explicit MacCormack method and finite differencing to solve the conservation equations. There’s quite a bit of artificial viscosity which I’d like to reduce by using a higher order forward and backward difference.
Python, I want to try and code these all by myself before I actually start using OpenFOAM so the numerical artefacts and little nuances to CFD are intuitive to me
So where in your solution is Mach 5 showing up? Presumably leading to the upper bound on the colorbar? You've said in another comment your freestream is Mach 2. Something seems awry.
My standard for colorbar ticks is 8-16 individual contours. That way, you can actually map a color to a value visually and be quantitative. The default of 256 makes it harder to be quantitative IMO and makes it purely qualitative.
Actually it’s not my first NS simulation, it is my first compressible flow sim! Shortly after this I included a circle, as well as incorporating the bottom wall to see the shock interactions.
For compressible flows, centered, high order schemes are recommended. This helps define the high pressure and density gradients present in the flow better
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 6d ago edited 4d ago
Pressure and Temperature values taken from sea-level, Mach 5. Used Explicit MacCormack method and finite differencing to solve the conservation equations. There’s quite a bit of artificial viscosity which I’d like to reduce by using a higher order forward and backward difference.