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I'm trying to solve this Burger's equation and continuity with a pressure forcing term. Below is the code snippet that I've tried already for the non-dimensionalized equations. The parameter B is all of the constants wrapped up. I've tried a few methods like ExplicitRungeKutta, StiffnessSwitching, BDF, and Automatic, but the error I receive is always:

NDSolve::ndsz: At t == 2.4983101830020135`*^-16, step size is effectively zero; singularity or stiff system suspected.

I don't really know how to fix this, so any help is appreciated!

BurgersAndContinuityEqns = 
  {r ne[r, t]* D[u[r, t],t] + ne[r, t] u[r, t] D[u[r, t]*r,r] == 
     -B D[r*ne[r, t], r], 
   r D[ne[r, t], r] + D[r u[r, t] ne[r, t], r] == 0, 
   u[r, ϵ] == 0, ne[r, ϵ] == Exp[-(r^2/2)]};

Here is the NDSolve snippet. I've tried putting the starting point off in time and space by machine epsilon, but no luck.

SolnBa =
esol = 
Block[{ϵ = $MachineEpsilon}, 
NDSolve[
BurgersAndContinuityEqns /. B -> 157.59, 
{u[r, t], ne[r, t]}, {r, ϵ, 5}, {t, ϵ, 0.18}, 
Method -> {"StiffnessSwitching"}]]

Again, any help that can be provided is much appreciated!

lstriker
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    What's the b.c. in $r$ direction? Notice you still need artificial b.c. representing infinity even if you're just solving an initial value problem. The "b.c." added automatically by NDSolve is almost always improper, check this post for more information. – xzczd Mar 24 '18 at 17:34

0 Answers0