Add basic physical scaling and Knudsen quality criterion

The paper "Automatic grid refinement criterion for lattice Boltzmann method" [2015]
by Lagrava et al. describes a criterion for measuring the local simulation quality
using a comparison of the theoretical Knudsen number and the quotient of the cells's
non-equilibrium and equilibrium function.

While this criterion was developed to enable automatic selection of areas to be refined,
it also offers a interesting and unique perspective on the fluid structure.

As the criterion requires calculation of the modeled Reynolds-, Mach- and Knudsen-numbers
I took the time to set up the basics for scaling the simulation to actually model a physical
system. Or rather calculating which physical model is represented by the chosen resolution
and relaxation time.

[2015]: https://arxiv.org/abs/1507.06767

1 files changed, 13 insertions, 4 deletions

diff --git a/src/shader/code/vertex.glsl b/src/shader/code/vertex.glsl
index 676b68e..7851292 100644
--- a/src/shader/code/vertex.glsl
+++ b/src/shader/code/vertex.glsl
@@ -10,7 +10,8 @@ out VS_OUT {
 uniform uint nX;
 uniform uint nY;
 
-const float displayAmplifier = 3.0;
+const float velocityDisplayAmplifier = 3.0;
+const int   qualityDisplayRestrictor = 6;
 
 float unit(float x) {
 	return 1.0/(1.0+exp(-x));
@@ -40,6 +41,14 @@ bool isWallFrontier(int material) {
 	return material == 2 || material == 3;
 }
 
+float restrictedQuality(float quality) {
+	if ( quality < 0.0 ) {
+		return 0.0;
+	} else {
+		return min(1.0, quality / qualityDisplayRestrictor);
+	}
+}
+
 void main() {
 	const vec2 idx = fluidVertexAtIndex(gl_VertexID);
 
@@ -58,9 +67,9 @@ void main() {
 		vs_out.color = vec3(0.0, 0.0, 0.0);
 	} else {
 		vs_out.color = mix(
-			vec3(-0.5, 0.0, 1.0),
-			vec3( 1.0, 0.0, 0.0),
-			displayAmplifier * norm(VertexPosition.xy)
+			vec3(0.0, 1.0, 0.0),
+			vec3(1.0, 0.0, 0.0),
+			restrictedQuality(VertexPosition.y)
 		);
 	}
 }