Draft: Wall law

Implementation of a wall law

lbmpy/boundaries/wall_treatment/spaldings_law.py

+import sympy as sp
+
+
+def spaldings_law(u_plus, y_plus, kappa=0.41, B=5.5):
+    """
+    Returns a symbolic expression for spaldings law
+
+    Args:
+        u_plus: velocity nondimensionalized by the friction velocity u_tau
+        y_plus: distances from the wall nondimensionalized by the friction velocity u_tau
+        kappa: free parameter
+        B: free parameter
+    """
+    k_times_u = kappa * u_plus
+    fraction_1 = (k_times_u ** 2) / 2
+    fraction_2 = (k_times_u ** 3) / 6
+    return u_plus + sp.exp(-kappa * B) * (sp.exp(k_times_u) - 1 - k_times_u - fraction_1 - fraction_2) - y_plus