add example plot

examples/fluid/rectangular_tank_2d.jl

@@ -1,5 +1,6 @@
 using TrixiParticles
 using OrdinaryDiffEq
+using PyPlot
 
 # ==========================================================================================
 # ==== Resolution
@@ -84,18 +85,23 @@ sol = solve(ode, RDPK3SpFSAL49(),
             dtmax=1e-2, # Limit stepsize to prevent crashing
             save_everystep=false, callback=callbacks);
 
+# Example for using interpolation
+#######################################################################################
+
+# interpolate_point can be used to interpolate the properties of the 'fluid_system' with the original kernel and smoothing_length
 println(interpolate_point([1.0, 0.01], semi, fluid_system, sol))
+# or with an increased smoothing_length smoothing the result
 println(interpolate_point([1.0, 0.01], semi, fluid_system, sol,
                           smoothing_length=2.0 * smoothing_length))
-println(interpolate_point([1.0, 0.1], semi, fluid_system, sol))
-println(interpolate_point([1.0, 0.1], semi, fluid_system, sol,
-                          smoothing_length=2.0 * smoothing_length))
+
+
+# a point outside of the domain will result in properties with value 0
+# on the boundary a result can still be obtained
 println(interpolate_point([1.0, 0.0], semi, fluid_system, sol))
-println(interpolate_point([1.0, 0.0], semi, fluid_system, sol,
-                          smoothing_length=2.0 * smoothing_length))
+# slightly befind the result is 0
 println(interpolate_point([1.0, -0.01], semi, fluid_system, sol))
-println(interpolate_point([1.0, -0.05], semi, fluid_system, sol))
 
+# multiple points can be interpolated by providing an array
 println(interpolate_point([
                               [1.0, 0.01],
                               [1.0, 0.1],
@@ -104,7 +110,27 @@ println(interpolate_point([
                               [1.0, -0.05],
                           ], semi, fluid_system, sol))
 
-println(interpolate_line([1.0, -0.05], [1.0, 1.0], 5, semi, fluid_system,
-                         sol))
-println(interpolate_line([1.0, -0.05], [1.0, 1.0], 5, semi, fluid_system,
-                         sol, endpoint=false))
+# it is also possible to interpolate along a line
+result = interpolate_line([1.0, -0.05], [1.0, 1.0], 10, semi, fluid_system, sol)
+result_endpoint = interpolate_line([1.0, -0.05], [1.0, 1.0], 10, semi, fluid_system, sol,
+                                    endpoint=false)
+# Extract densities and coordinates for plotting
+densities = [r.density for r in result]
+coords = [r.coord[2] for r in result]  # Assuming you want to plot against the y-coordinate
+
+densities_endpoint = [r.density for r in result_endpoint]
+coords_endpoint = [r.coord[2] for r in result_endpoint]
+
+# Create the plot
+figure()
+plot(coords, densities, marker="o", linestyle="-", label="With Endpoint")
+plot(coords_endpoint, densities_endpoint, marker="x", linestyle="--", label="Without Endpoint")
+
+# Add labels and legend
+xlabel("Y-Coordinate")
+ylabel("Density")
+title("Density Interpolation Along a Line")
+legend()
+
+# Display the plot
+show()