Please run the attached code. The density plot has some artifacts on it (The light blue parts around the circle) Is there a way to resolve this issue. The density plot is showing velocity of a liquid passing through the channel. Regards.
[CapitalOmega] =
ImplicitRegion[
0 <= x <= 2.0 &&
0 <= y <=
0.48208 && ! (x >= 1.0 && y <= 0.19) && ! (x >= 1.0 &&
y >= 0.31) && ! ((x - 0.76)^2 + (y - 0.24104)^2 <=
0.238125^2), {x, y}];
RegionPlot[[CapitalOmega], AspectRatio -> Automatic, ImageSize -> 300]
stokesFlowOperator = {Div[({{-1, 0}, {0, -1}}.Grad[
u[x, y], {x, y}]), {x, y}] +
\!(*SuperscriptBox[(w),
TagBox[
RowBox[{"(",
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None])[x, y],
Div[({{-1, 0}, {0, -1}}.Grad[v[x, y], {x, y}]), {x, y}] +
\!(*SuperscriptBox[(w),
TagBox[
RowBox[{"(",
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None])[x, y],
\!(*SuperscriptBox[(v),
TagBox[
RowBox[{"(",
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None])[x, y] +
\!(*SuperscriptBox[(u),
TagBox[
RowBox[{"(",
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None])[x, y]};
Subscript[[CapitalGamma],
D] = {DirichletCondition[{u[x, y] == -1, v[x, y] == 0}, x == 0.],
DirichletCondition[{u[x, y] == 1., v[x, y] == 0}, 0 < x < 2.0],
DirichletCondition[w[x, y] == 0.1, x == 2.0]};
{xVel, yVel, pressure} =
NDSolveValue[{stokesFlowOperator == {0, 0, 0},
Subscript[[CapitalGamma], D]}, {u, v,
w}, {x, y} [Element] [CapitalOmega],
Method -> {"FiniteElement",
"InterpolationOrder" -> {u -> 2, v -> 2, w -> 1}}];
rmf = RegionMember[[CapitalOmega]];
Show[BoundaryDiscretizeRegion[[CapitalOmega]],
DensityPlot[{xVel[x, y], yVel[x, y]}, {x, 0, 2.0}, {y, 0, 0.48208},
RegionFunction -> Function[{x, y}, rmf[{x, y}]],
AspectRatio -> Automatic, PlotLegends -> Automatic,
ColorFunction -> ColorData["BlueGreenYellow"], PlotPoints -> 20],
ImageSize -> 1000]
Attachments: