From 7ebfbecd7485ab25418bd35ff0193069568fb48e Mon Sep 17 00:00:00 2001
From: Andrew Heather <a.heather@opencfd.co.uk>
Date: Tue, 1 Dec 2015 10:26:23 +0000
Subject: [PATCH] Turbulence - updated Spalart-Allmaras IDDES to be consistent
 with reference

---
 .../SpalartAllmarasIDDES.C                    | 29 +++++++++++++------
 .../SpalartAllmarasIDDES.H                    |  2 +-
 2 files changed, 21 insertions(+), 10 deletions(-)

diff --git a/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.C b/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.C
index 5f94e2731d..40ea5c9e6a 100644
--- a/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.C
+++ b/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.C
@@ -37,6 +37,7 @@ namespace LESModels
 template<class BasicTurbulenceModel>
 tmp<volScalarField> SpalartAllmarasIDDES<BasicTurbulenceModel>::alpha() const
 {
+    // Equation 9 (plus limits)
     return max
     (
         0.25 - this->y_/static_cast<const volScalarField&>(IDDESDelta_.hmax()),
@@ -51,6 +52,7 @@ tmp<volScalarField> SpalartAllmarasIDDES<BasicTurbulenceModel>::ft
     const volScalarField& magGradU
 ) const
 {
+    // Equation 13
     return tanh(pow3(sqr(ct_)*rd(this->nut_, magGradU)));
 }
 
@@ -61,6 +63,7 @@ tmp<volScalarField> SpalartAllmarasIDDES<BasicTurbulenceModel>::fl
     const volScalarField& magGradU
 ) const
 {
+    // Equation 13
     return tanh(pow(sqr(cl_)*rd(this->nu(), magGradU), 10));
 }
 
@@ -90,11 +93,12 @@ tmp<volScalarField> SpalartAllmarasIDDES<BasicTurbulenceModel>::rd
 // * * * * * * * * * * * * Protected Member Functions  * * * * * * * * * * * //
 
 template<class BasicTurbulenceModel>
-tmp<volScalarField> SpalartAllmarasIDDES<BasicTurbulenceModel>::fd
+tmp<volScalarField> SpalartAllmarasIDDES<BasicTurbulenceModel>::fdt
 (
     const volScalarField& magGradU
 ) const
 {
+    // Related to equation 16
     return 1 - tanh(pow3(8*rd(this->nuEff(), magGradU)));
 }
 
@@ -111,21 +115,28 @@ tmp<volScalarField> SpalartAllmarasIDDES<BasicTurbulenceModel>::dTilda
     const volScalarField expTerm(exp(sqr(alpha)));
     const volScalarField magGradU(mag(gradU));
 
-    tmp<volScalarField> fHill =
+    // Equation 9
+    tmp<volScalarField> fB = min(2*pow(expTerm, -9.0), scalar(1));
+
+    // Equation 11
+    tmp<volScalarField> fe1 =
         2*(pos(alpha)*pow(expTerm, -11.09) + neg(alpha)*pow(expTerm, -9.0));
 
-    tmp<volScalarField> fStep = min(2*pow(expTerm, -9.0), scalar(1));
-    const volScalarField fHyb(max(1 - fd(magGradU), fStep));
-    tmp<volScalarField> fAmp = 1 - max(ft(magGradU), fl(magGradU));
-    tmp<volScalarField> fRestore = max(fHill - 1, scalar(0))*fAmp;
+    // Equation 12
+    tmp<volScalarField> fe2 = 1 - max(ft(magGradU), fl(magGradU));
 
+    // Equation 10
     const volScalarField psi(this->psi(chi, fv1));
+    tmp<volScalarField> fe = max(fe1 - 1, scalar(0))*psi*fe2;
 
+    // Equation 16
+    const volScalarField fdTilda(max(1 - fdt(magGradU), fB));
+
+    // Equation 17 (plus limits)
     return max
     (
-        dimensionedScalar("SMALL", dimLength, SMALL),
-        fHyb*(1 + fRestore*psi)*this->y_
-      + (1 - fHyb)*psi*this->CDES_*this->delta()
+        fdTilda*(1 + fe)*this->y_ + (1 - fdTilda)*psi*this->CDES_*this->delta(),
+        dimensionedScalar("SMALL", dimLength, SMALL)
     );
 }
 
diff --git a/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.H b/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.H
index 1db9a9fad8..f146bf1dbf 100644
--- a/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.H
+++ b/src/TurbulenceModels/turbulenceModels/DES/SpalartAllmarasIDDES/SpalartAllmarasIDDES.H
@@ -92,7 +92,7 @@ class SpalartAllmarasIDDES
         ) const;
 
         //- Delay function
-        tmp<volScalarField> fd(const volScalarField& magGradU) const;
+        tmp<volScalarField> fdt(const volScalarField& magGradU) const;
 
         // Disallow default bitwise copy construct and assignment
         SpalartAllmarasIDDES(const SpalartAllmarasIDDES&);