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Christian87 January 31, 2013 13:32

Impermeable Wall BC Euler Equations
 
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Hello,

as the title says I tried to implement an impermeable wall for my 2D Euler equiation Richtmyer FV solver. For validation purposes I'm currently doing calculations for easy cases like the wedge (see pic).

This wedge has an angle of 20 and the freestream Mach number is 3.3. According to the analytical solution (dotted line) there should be a Mach number of 2.75 downstream of the shock.

Unfortunately, I get a Mach number of around 2.3 and I'm blaming my wall bc since the grid should be fine (see pic). If you wonder why I approximated the apex by a parabola, it's only to exclude errors induced by the singularity of the apex. My first grid had an even stronger deviation.

The bcs at the left side is supersonic, respectively supersonic outlet at the right side.

The variables on the wall (j=1) are obtained by extrapolation of the values of the interior

q1bc=q1(i,j+1)
q4bc=q4(i,j+1)

q2bc=q2(i,j+1)
q3bc=q3(i,j+1)

In the next step I transfrom the velocity by using the tangential vector, which I obtain by

t=[x(i+1,j=1)-x(i-1,j=1);y(i+1,j=1)-y(i-1,j=1)];

taking the neighbour wall nodes. After that I norm t and calculate the wall velocity with the dot product (*) as

u_w = (t*[q2bc ; q3bc ]) t

and finally obtain my values for

q2bc=uw(1,1) and q3bc=uw(2,1).

This gave me good results for the Laval nozzle but here for the wedge I think this is the only potential source for the deviation.

Any hints or advice is strongly appreciated. Thank you for reading.


Christian


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