mrtCollision operator in OpenLB

[Eric]

Dear OpenLB team,

I have a question about the mrtCollision solver implemented in OpenLB. As far as I understand, the original code first compute momenta and momenta_eq, but I can see that only 6 of 9 parameters are calculated here:

Code:

template<typename T>
38 struct mrtHelpers<T, descriptors::MRTD2Q9Descriptor> {
39
41 static void computeEquilibrium( T momentaEq[9],
42 T rho, const T u[2],
43 const T uSqr )
44 {
45 // momentaEq[0] = T();
46 momentaEq[1] = -(T)2*rho + (T)3*uSqr;
47 momentaEq[2] = rho – (T)3*uSqr;
48 // momentaEq[3] = T();
49 momentaEq[4] = -u[0];
50 // momentaEq[5] = T();
51 momentaEq[6] = -u[1];
52 momentaEq[7] = u[0]*u[0] – u[1]*u[1];
53 momentaEq[8] = u[0]*u[1];
54 }
55
57 static void computeMomenta(T momenta[9], Cell<T,MRTD2Q9Descriptor> &cell)
58 {
59 // momenta[0] = cell[0] + cell[1] + cell[2] + cell[3] +
60 // cell[4] + cell[5] + cell[6] + cell[7] + cell[8] + (T)1;
61
62 momenta[1] = -(T)4*cell[0] +(T)2*cell[1] – cell[2] + (T)2*cell[3] – cell[4] +
63 (T)2*cell[5] – cell[6] + (T)2*cell[7] – cell[8] – (T)2;
64
65 momenta[2] = (T)4*cell[0] + cell[1] – (T)2*cell[2] + cell[3] – (T)2*cell[4] +
66 cell[5] – (T)2*cell[6] + cell[7] – (T)2*cell[8] + (T)1;
67
68 // momenta[3] = – cell[1] – cell[2] – cell[3] +
69 // cell[5] + cell[6] + cell[7];
70
71 momenta[4] = – cell[1] + (T)2*cell[2] – cell[3] +
72 cell[5] – (T)2*cell[6] + cell[7];
73
74 // momenta[5] = cell[1] – cell[3] – cell[4] –
75 // cell[5] + cell[7] + cell[8];
76
77 momenta[6] = cell[1] – cell[3] + (T)2*cell[4] –
78 cell[5] + cell[7] – (T)2*cell[8];
79
80 momenta[7] = cell[2] – cell[4] + cell[6] – cell[8];
81
82 momenta[8] = – cell[1] + cell[3] – cell[5] + cell[7];
83 }

May I ask why there’s no need to calculate index 0,3, and 5? I guess it might help reduce computation time, but when updating

Code:

cell[iPop] -= invM_S[iPop][jPop]*momX

the deleted element in invM_S is not always 0. So will this affect the computation?

P.S. Could you also explain why we need to add 2 to the momenta[1] when calculating momenta in the following code? I understand this is energy momenta, but the matrix multiplication should not produce 2?

Code:

62 momenta[1] = -(T)4*cell[0] +(T)2*cell[1] – cell[2] + (T)2*cell[3] – cell[4] +
63 (T)2*cell[5] – cell[6] + (T)2*cell[7] – cell[8] – (T)2;

Looking forward to hearing from you.

Best regards,
Eric

[mathias]

Dear Eric,

1/ Actually 0,3, and 5 are ZERO:

template<typename T>
const T MRTD2Q9DescriptorBase<T>::S[MRTD2Q9DescriptorBase<T>::q_] =
{ T(), (T)1.1, (T)1.1, T(), (T)1.1, T(), (T)1.1, T(), T() };
// s7=s8 to have a shear viscosity nu
// and the bulk viscosity depends on s2.

2/ In openLB we save f_OLB = f – f^eq. So \sum_q f_OLB + 1 = rho.

Best
Mathias

[Eric]

Dear Mathias,

Thank you very much for you explanation!

Best regards,
Eric

[Author]

Posts