Fix findYPlus routine. idaholab#27800

modules/navier_stokes/src/base/NavierStokesMethods.C

@@ -69,13 +69,20 @@ findUStar(const ADReal & mu, const ADReal & rho, const ADReal & u, const Real di
 
   const ADReal nu = mu / rho;
 
-  ADReal u_star = std::sqrt(nu * u / dist);
+  // Wall-function linearized guess
+  const Real a_c = 1 / NS::von_karman_constant;
+  const ADReal b_c =
+      1 / NS::von_karman_constant * (std::log(NS::E_turb_constant * dist / mu) + 1.0);
+  const ADReal c_c = u;
+
+  /// This is important to reduce the number of nonlinear iterations
+  ADReal u_star = (-b_c + std::sqrt(std::pow(b_c, 2) + 4.0 * a_c * c_c)) / (2.0 * a_c);
 
   // Newton-Raphson method to solve for u_star (friction velocity).
   for (int i = 0; i < MAX_ITERS; ++i)
   {
-    ADReal residual = u_star / NS::von_karman_constant * std::log(u_star * dist / (0.111 * nu)) - u;
-    ADReal deriv = (1 + std::log(u_star * dist / (0.111 * nu))) / NS::von_karman_constant;
+    ADReal residual = u_star / NS::von_karman_constant * std::log(NS::E_turb_constant * u_star * dist / nu) - u;
+    ADReal deriv = (1 + std::log(NS::E_turb_constant * u_star * dist / nu)) / NS::von_karman_constant;
     ADReal new_u_star = std::max(1e-20, u_star - residual / deriv);
 
     Real rel_err = std::abs((new_u_star.value() - u_star.value()) / new_u_star.value());
@@ -114,7 +121,7 @@ findyPlus(const ADReal & mu, const ADReal & rho, const ADReal & u, const Real di
   {
     yPlusLast = yPlus;
     yPlus = (kappa_time_Re + yPlus) / (1.0 + std::log(NS::E_turb_constant * yPlus));
-  } while (rev_yPlusLam * (yPlus - yPlusLast) > REL_TOLERANCE && ++iters < MAX_ITERS);
+  } while ( std::abs(rev_yPlusLam * (yPlus - yPlusLast)) > REL_TOLERANCE && ++iters < MAX_ITERS);
 
   return std::max(0.0, yPlus);
 }