Add more NRBC treatment in the 1D Euler solver

[yungyuc]

PR #326 implemented a NRBC treatment for the 1D Euler solver. There are other variants that we should try.

The associated issue for adding notes: solvcon/mmnote#31

[Gene0315]

In the CESE method, the points j on boundary have a lack of data from outside points, so it is difficult to predict their value at next time step. Maybe one possible approach is to extend the half dx cell point outside the boundary (red cross icon in the diagram). Then, these j points on boundary will can be solved. Alternatively, we can avoid the situation by excluding these points j when plotting.

[yungyuc]

@Gene0315 I agree that we can also make the plotting look nicer. That can use a different issue to track. Could you please create one? (And associate that one with this.)

[Gene0315]

I try to use the second NRBC method with lambda=0. I think the zig-zag array could be shown simpely in the figure. The number 0~3 is the first index of m_so0 and m_so1.

As I see it, the value at boundary point, such as m_so0(0, 1:3) and m_so1(0, 1:3), should be equal to the m_so0(1, 1:3) and m_so1(1, 1:3) before calculating the new value in next time step. Thus, I revised the “treat_boundary_so0()” and “treat_boundary_so1()” in “Euler1DCore.cp”.

And then, I changed the sequence of “treat_boundary_so0”, “treat_boundary_so1”, and “march_half_so0”. The sections I changed including

• wrap_onedim.cpp

• core.hpp

• wrap_spacetime.cpp

• wrap_spacetime.hpp

• test_onedim_euler.py

• test_spacetime_solution.py

But, after 200 time steps, the result showed

[yungyuc]

@Gene0315 I agree that we can also make the plotting look nicer. That can use a different issue to track. Could you please create one? (And associate that one with this.)

@Gene0315 I wonder what is your response to this request?

And please do not attach images for showing code or diff like in your comment #330 (comment) . When you want to show plain text, use plain text format of markdown. For example, you can quote code diff like:

diff --git a/cpp/modmesh/onedim/Euler1DCore.cpp b/cpp/modmesh/onedim/Euler1DCore.cpp
index 8065d79..2eb9bde 100644
--- a/cpp/modmesh/onedim/Euler1DCore.cpp
+++ b/cpp/modmesh/onedim/Euler1DCore.cpp
@@ -179,7 +179,7 @@ void Euler1DCore::treat_boundary_so1()
     // Set outside value from inside value.
     {
         // Left boundary.
-        size_t const ic = 1;
+        size_t const ic = 0;
         m_so1(ic, 0) = m_so1(ic + 1, 0);
         m_so1(ic, 1) = m_so1(ic + 1, 1);
         m_so1(ic, 2) = m_so1(ic + 1, 2);

Code pasted in an image cannot be searched and is useless. We should not do it in GitHub.

It is easier to discuss for your question in #330 (comment) in a pull request. Please create one for it.