Defaults for the couette_flow_2d demo are (1) small and (2) double precision.
If your GPU has good support for double precision (fp64), and lots of memory, you can use gmsh to generate a bigger mesh for that demo.
E.g., the script below makes a mesh with 25,000 quadrilateral elements. Adjust params to suit your GPU (and patience).
lc = 1.00; // Q: 25,4532; [X] Recombine all triangular meshes
xmin = -100.0;
ymin = 0.0;
xmax = 100.0;
ymax = 100.0;
zall = 0.0;
Point(1) = {xmin, ymin, zall, lc};
Point(2) = {xmax, ymin, zall, lc};
Point(3) = {xmax, ymax, zall, lc};
Point(4) = {xmin, ymax, zall, lc};
//---------------------------------------
Line(1) = {1,2};
Line(2) = {2,3};
Line(3) = {3,4};
Line(4) = {4,1};
LL=newll; Line Loop(LL) = {1,2,3,4};
PS=news; Plane Surface(PS) = {LL};
// optionally, recombine triangles to quads
Recombine Surface {PS};
Physical Surface("Fluid", 1) = {PS};
Physical Line("periodic_0_r", 2) = {2};
Physical Line("periodic_0_l", 3) = {4};
Physical Line("bcwalllower", 4) = {1};
Physical Line("bcwallupper", 5) = {3};