Dear PETSC users,
I am a newbie to PETSC and I try to understand it. My first attempt is
to solve 2D laminar boundary layer equations:
u*du/dx +v*du/dy = Ue*(dUe/dx). -nu*d2u/dy2
dudx + dvdy = 0
B.C.:
y=0: u=0, v=0
y=H: u(x)=Ue(x)
Where H is height of the domain, Ue(x) is edge velocity given by a
potential flow solver. I assume Ue(x)=10.0
I have several questions regarding the workflow in PETSC, I took SNES
example29 (2D cavity flow) and I tried to modify it:
1) There are vectors x and f. I suppose vector x to represent the values
of velocity and vector f to represent velocity residuals. Please is this
correct?
Based on example29 and my assumption, I calculated the velocity:
dhx = (PetscReal)(info->mx-1); dhy = (PetscReal)(info->my-1);
dx = 1.0/dhx; dy = 1./dhy;
u = x[j][i].u;
v = x[j][i].v;
dudx = (x[j][i+1].u - x[j][i-1].u)/2.0/dx;
dudy = (x[j+1][i].u - x[j-1][i].u)/2.0/dy;
dvdy = (x[j+1][i].v - x[j-1][i].v)/2.0/dy;
d2udy2 = (-2.0*u + x[j-1][i].u + x[j+1][i].u)/dy/dy;
/* U velocity */
f[j][i].u = u*dudx +v*dudy -Ue*dUedx -nu*d2udy2;
/* V velocity */
f[j][i].v = dudx + dvdy;
The code does not work. With initial conditions x[j][i].u=Ue; and
x[0][i].u=0.0; the result is the same as the initial conditions.
2) In SNES example29, there are boundary conditions specified on vector
f? For example:
/* Test whether we are on the top edge of the global array */
if (yinte == info->my) {
j = info->my - 1;
yinte = yinte - 1;
/* top edge */
for (i=info->xs; i<info->xs+info->xm; i++) {
f[j][i].u = x[j][i].u - lid;
f[j][i].v = x[j][i].v;
I don't understand the last two lines. I just deleted the conditions for
left and right edges and replaced f[j][i].u = x[j][i].u - lid; with
f[j][i].u = x[j][i].u - Ue;
3) Please could someone explain the normalization on following lines?
(Taken from example 29)
/*
Define mesh intervals ratios for uniform grid.
Note: FD formulae below are normalized by multiplying through by
local volume element (i.e. hx*hy) to obtain coefficients O(1)
in two dimensions.
*/
dhx = (PetscReal)(info->mx-1); dhy = (PetscReal) (info->my-1);
hx = 1.0/dhx; hy = 1.0/dhy;
hxdhy = hx*dhy; hydhx = hy*dhx;
Thanks in advance & Kind regards
Pavel Schor
PhD. student, Institute of aerospace engineering, Brno University of
technology
