Momentum sources¶

You can add additional momentum sources to the simulations which can be useful for MMS testing (Method of Manufactured Solutions). An example from the variable density disk test case included in the Ocellaris source code repository can be seen below (this MMS test was taken from 1).

momentum_sources:
-   name: MMS
    degree: 2
    cpp_code:
    -   Q*nu*sin(sin(t))*cos(t) - (x[0]*cos(t)*cos(t) - x[1]*sin(t))*(Q*sqrt(x[0]*x[0] + x[1]*x[1])*cos(sin(t) - atan2(x[1], x[0])) + 1 + Q) + sin(t)*sin(x[1])*cos(x[0])
    -   -Q*nu*cos(t)*cos(sin(t)) - (x[0]*sin(t) + x[1]*cos(t)*cos(t))*(Q*sqrt(x[0]*x[0] + x[1]*x[1])*cos(sin(t) - atan2(x[1], x[0])) + 1 + Q) + sin(t)*sin(x[0])*cos(x[1])

degree

The polynomial degree of the function used to represent the momentum source C++ expression

Citations

1

J. Guermond and A. Salgado. Error analysis of a fractional time-stepping technique for incompressible flows with variable density. SIAM Journal on Numerical Analysis, 49(3):917–944, 2011. doi:10.1137/090768758.