ProcessWSS.cpp

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////////////////////////////////////////////////////////////////////////////////
//
//  File: ProcessWSS.cpp
//
//  For more information, please see: http://www.nektar.info/
//
//  The MIT License
//
//  Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
//  Department of Aeronautics, Imperial College London (UK), and Scientific
//  Computing and Imaging Institute, University of Utah (USA).
//
//  License for the specific language governing rights and limitations under
//  Permission is hereby granted, free of charge, to any person obtaining a
//  copy of this software and associated documentation files (the "Software"),
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//
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//  OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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//
//  Description: Computes wss field.
//
////////////////////////////////////////////////////////////////////////////////

#include <string>
#include <iostream>
using namespace std;

#include "ProcessWSS.h"

#include <LibUtilities/BasicUtils/SharedArray.hpp>
#include <LibUtilities/BasicUtils/ParseUtils.hpp>
#include <MultiRegions/ExpList.h>

namespace Nektar
{
namespace Utilities
{

ModuleKey ProcessWSS::className =
    GetModuleFactory().RegisterCreatorFunction(
        ModuleKey(eProcessModule, "wss"),
        ProcessWSS::create, "Computes wall shear stress field.");

ProcessWSS::ProcessWSS(FieldSharedPtr f) : ProcessModule(f)
{
    m_config["bnd"] = ConfigOption(false,"All","Boundary to be extracted");
    m_config["addnormals"] = ConfigOption(true,"NotSet","Add normals to output");
    f->m_writeBndFld = true;
    f->m_declareExpansionAsContField = true;
    m_f->m_fldToBnd = false;
}

ProcessWSS::~ProcessWSS()
{
}

void ProcessWSS::Process(po::variables_map &vm)
{
    if (m_f->m_verbose)
    {
        cout << "ProcessWSS: Calculating wall shear stress..." << endl;
    }

    m_f->m_addNormals = m_config["addnormals"].m_beenSet;

    // Set up Field options to output boundary fld
    string bvalues =  m_config["bnd"].as<string>();

    if(bvalues.compare("All") == 0)
    {
        Array<OneD, const MultiRegions::ExpListSharedPtr>
            BndExp = m_f->m_exp[0]->GetBndCondExpansions();

        for(int i = 0; i < BndExp.num_elements(); ++i)
        {
            m_f->m_bndRegionsToWrite.push_back(i);
        }
    }
    else
    {
        ASSERTL0(ParseUtils::GenerateOrderedVector(bvalues.c_str(),
                                                   m_f->m_bndRegionsToWrite),"Failed to interpret range string");
    }

    NekDouble kinvis = m_f->m_session->GetParameter("Kinvis");

    int i, j;
    int spacedim  = m_f->m_graph->GetSpaceDimension();
    if ((m_f->m_fielddef[0]->m_numHomogeneousDir) == 1 ||
        (m_f->m_fielddef[0]->m_numHomogeneousDir) == 2)
    {
        spacedim += m_f->m_fielddef[0]->m_numHomogeneousDir;
    }

    int nfields = m_f->m_fielddef[0]->m_fields.size();
    ASSERTL0(m_f->m_fielddef[0]->m_fields[0] == "u","Implicit assumption that input is in incompressible format of (u,v,p) or (u,v,w,p)");

    if (spacedim == 1)
    {
        ASSERTL0(false, "Error: wss for a 1D problem cannot "
                 "be computed");
    }

    int newfields = spacedim + 1;
    int nshear    = spacedim + 1;
    int nstress   = spacedim*spacedim;
    int ngrad     = spacedim*spacedim;

    Array<OneD, Array<OneD, NekDouble> > velocity(nfields), grad(ngrad), fgrad(ngrad);
    Array<OneD, Array<OneD, NekDouble> > stress(nstress), fstress(nstress);
    Array<OneD, Array<OneD, NekDouble> > fshear(nshear);
    
    Array<OneD, MultiRegions::ExpListSharedPtr> BndExp(newfields);
    Array<OneD, MultiRegions::ExpListSharedPtr> BndElmtExp(nfields);
    
    // Extract original fields to boundary (for output)
    for (int i = 0; i < m_f->m_exp.size(); ++i)
    {
        m_f->m_exp[i]->FillBndCondFromField();
    }

    m_f->m_exp.resize(nfields + newfields);
    string var = "u";
    for(i = 0; i < newfields; ++i)
    {
        m_f->m_exp[nfields + i] = m_f->AppendExpList(m_f->m_fielddef[0]->m_numHomogeneousDir, var);
    }

    if(spacedim == 2)
    {
        m_f->m_fielddef[0]->m_fields.push_back("Shear_x");
        m_f->m_fielddef[0]->m_fields.push_back("Shear_y");
        m_f->m_fielddef[0]->m_fields.push_back("Shear_mag");
    }
    else
    {
        m_f->m_fielddef[0]->m_fields.push_back("Shear_x");
        m_f->m_fielddef[0]->m_fields.push_back("Shear_y");
        m_f->m_fielddef[0]->m_fields.push_back("Shear_z");
        m_f->m_fielddef[0]->m_fields.push_back("Shear_mag");
    }

    // Loop over boundaries to Write
    for(int b = 0; b < m_f->m_bndRegionsToWrite.size(); ++b)
    {
        int bnd = m_f->m_bndRegionsToWrite[b];
        // Get expansion list for boundary and for elements containing this bnd
        for(i = 0; i < newfields; i++)
        {
            BndExp[i]   = m_f->m_exp[nfields + i]->UpdateBndCondExpansion(bnd);
        }
        for(i = 0; i < spacedim; i++)
        {
            m_f->m_exp[i]->GetBndElmtExpansion(bnd, BndElmtExp[i]);
        }
        
        // Get number of points in expansions
        int nqb = BndExp[0]->GetTotPoints();
        int nqe = BndElmtExp[0]->GetTotPoints();
        
        // Initialise local arrays for the velocity gradients, and stress components
        // size of total number of quadrature points for elements in this bnd
        for(i = 0; i < ngrad; ++i)
        {
            grad[i] = Array<OneD, NekDouble>(nqe);
        }

        for(i = 0; i < nstress; ++i)
        {
            stress[i] = Array<OneD, NekDouble>(nqe);
        }

        // initialise arrays in the boundary
        for(i = 0; i < nstress; ++i)
        {
            fstress[i] = Array<OneD, NekDouble>(nqb);
        }

        for(i = 0; i < ngrad; ++i)
        {
            fgrad[i] = Array<OneD, NekDouble>(nqb);
        }

        for(i = 0; i < nshear; ++i)
        {
            fshear[i] = Array<OneD, NekDouble>(nqb, 0.0);
        }

        //Extract Velocities
        for(i = 0; i < spacedim; ++i)
        {
            velocity[i] = BndElmtExp[i]->GetPhys();
        }

        //Compute gradients (velocity correction scheme method)
        for(i = 0; i < spacedim; ++i)
        {
            if (spacedim == 2)
            {
                BndElmtExp[i]->PhysDeriv(velocity[i],grad[i*spacedim+0],
                                                     grad[i*spacedim+1]);
            }
            else
            {
                BndElmtExp[i]->PhysDeriv(velocity[i],grad[i*spacedim+0],
                                                     grad[i*spacedim+1],
                                                     grad[i*spacedim+2]);
            }
        }

         //Compute stress component terms  tau_ij = mu*(u_i,j + u_j,i)
        for(i = 0; i < spacedim; ++i)
        {
            for(j = 0; j < spacedim; ++j)
            {
                Vmath::Vadd(nqe, grad[i*spacedim+j], 1,
                                 grad[j*spacedim+i], 1,
                                 stress[i*spacedim+j], 1);
                
                Vmath::Smul(nqe, kinvis, stress[i*spacedim+j], 1,
                                           stress[i*spacedim+j], 1);
            }
        }

        // Get boundary stress values.
        for(j = 0; j < nstress; ++j)
        {
            m_f->m_exp[0]->ExtractElmtToBndPhys(bnd, stress[j],fstress[j]);
        }
        
        //Get normals
        Array<OneD, Array<OneD, NekDouble> > normals; 
        m_f->m_exp[0]->GetBoundaryNormals(bnd, normals);
        // Reverse normals, to get correct orientation for the body
        for(i = 0; i < spacedim; ++i)
        {
            Vmath::Neg(nqb, normals[i], 1);
        }

        //calculate wss, and update coeffs in the boundary expansion
        // S = tau_ij * n_j
        for(i = 0; i < spacedim; ++i)
        {
            for(j = 0; j < spacedim; ++j)
            {
                Vmath::Vvtvp(nqb,normals[j],1,fstress[i*spacedim+j],1,
                                              fshear[i],1,
                                              fshear[i],1);
            }
        }

        // T = S - (S.n)n
        for(i = 0; i < spacedim; ++i)
        {
            Vmath::Vvtvp(nqb,normals[i],1,fshear[i],1,
                                          fshear[nshear-1],1,
                                          fshear[nshear-1],1);
        }
        Vmath::Smul(nqb, -1.0, fshear[nshear-1], 1, fshear[nshear-1], 1);

        for (i = 0; i < spacedim; i++)
        {
            Vmath::Vvtvp(nqb,normals[i], 1, fshear[nshear-1], 1,
                                            fshear[i], 1,
                                            fshear[i], 1);
            BndExp[i]->FwdTrans(fshear[i], 
                                BndExp[i]->UpdateCoeffs());
        }

        // Tw
        Vmath::Zero(nqb, fshear[nshear-1], 1);
        for(i = 0; i < spacedim; ++i)
        {
            Vmath::Vvtvp(nqb,fshear[i],1,fshear[i],1,
                                         fshear[nshear-1],1,
                                         fshear[nshear-1],1);
        }
        Vmath::Vsqrt(nqb, fshear[nshear-1], 1, fshear[nshear-1], 1);
        BndExp[nshear-1]->FwdTrans(fshear[nshear-1], 
                                 BndExp[nshear-1]->UpdateCoeffs());
    }

}

}
}