Limiter

mathe5/klausurvorbereitung/limiter.m

+close all; clear; clc;
+
+theta = linspace(-4, 4, 1000);
+
+fig = figure(1);
+fig.WindowState = 'maximized';
+hold on;
+plot(theta, superbee(theta), 'DisplayName', 'superbee');
+plot(theta, minmod(theta), 'DisplayName', 'minmod');
+plot(theta, vanLeer(theta), 'DisplayName', 'van Leer');
+plot(theta, cslimiter(theta), 'DisplayName', 'Čada-Schmidtmann');
+title('Limiter functions');
+xlabel('\theta');
+ylabel('\phi');
+legend;
+hold off;
+
+function phi = t3(theta)
+    phi = (2 + theta) / 3;
+end
+
+function phi = cslimiter(theta)
+    phi = zeros(size(theta));
+    for i = 1:length(theta)
+        phi(i) = max(0, min(t3(theta(i)), max(-theta(i), min(2*theta(i), min(t3(theta(i)), 1.5)))));
+    end
+end
+
+function phi = superbee(theta)
+    phi = zeros(size(theta));
+    for i = 1:length(theta)
+        phi(i) = max(0, max(min(1, 2*theta(i)), min(2, theta(i))));
+    end
+end
+
+function phi = minmod(theta)
+    phi = zeros(size(theta));
+    for i = 1:length(theta)
+        phi(i) = max(0, min(1, theta(i)));
+    end
+end
+
+function phi = vanLeer(theta)
+    phi = zeros(size(theta));
+    for i = 1:length(theta)
+        phi(i) = (theta(i) + abs(theta(i))) / (1 + theta(i));
+    end
+end
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