Mapping.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: Mapping.h
//
// 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).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Abstract base class for mappings.
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_GLOBALMAPPING_MAPPING
#define NEKTAR_GLOBALMAPPING_MAPPING
 
#include <GlobalMapping/GlobalMappingDeclspec.h>
#include <LibUtilities/BasicUtils/FieldIO.h>
#include <LibUtilities/BasicUtils/NekFactory.hpp>
#include <LibUtilities/BasicUtils/SessionReader.h>
#include <LibUtilities/BasicUtils/SharedArray.hpp>
 
// Forward declaration
namespace Nektar::MultiRegions
{
class ExpList;
typedef std::shared_ptr<ExpList> ExpListSharedPtr;
} // namespace Nektar::MultiRegions
 
namespace Nektar::GlobalMapping
{
// Forward declaration
class Mapping;
 
/// A shared pointer to a Mapping object
GLOBAL_MAPPING_EXPORT typedef std::shared_ptr<Mapping> MappingSharedPtr;
 
/// Declaration of the mapping factory
typedef LibUtilities::NekFactory<
    std::string, Mapping, const LibUtilities::SessionReaderSharedPtr &,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &, const TiXmlElement *>
    MappingFactory;
 
/// Declaration of the mapping factory singleton
GLOBAL_MAPPING_EXPORT MappingFactory &GetMappingFactory();
 
/**
 * @class Mapping
 * @brief Base class for mapping to be applied to the coordinate system
 */
class Mapping
{
public:
    /// @brief Destructor
    GLOBAL_MAPPING_EXPORT virtual ~Mapping()
    {
    }
 
    /// @brief Initialise the mapping object
    GLOBAL_MAPPING_EXPORT void InitObject(
        const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
        const TiXmlElement *pMapping)
    {
        v_InitObject(pFields, pMapping);
    }
 
    /// @brief Replace the Expansion List used by the mapping
    GLOBAL_MAPPING_EXPORT void ReplaceField(
        const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields);
 
    /// @brief Return a pointer to the mapping, creating it on first call
    GLOBAL_MAPPING_EXPORT static MappingSharedPtr Load(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields);
 
    /// @brief Output function called when a chk or fld file is written
    GLOBAL_MAPPING_EXPORT void Output(
        LibUtilities::FieldMetaDataMap &fieldMetaDataMap,
        const std::string &outname);
 
    /////////////////////////////////////////////////////////////
    //
    //    Functions for transforming results to and from the
    //          Cartesian coordinate system
    //          (useful for pre and post processing)
    /////////////////////////////////////////////////////////////
 
    /// @brief Convert a contravariant vector to the Cartesian system
    GLOBAL_MAPPING_EXPORT void ContravarToCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    /// @brief Convert a covariant vector to the Cartesian system
    GLOBAL_MAPPING_EXPORT void CovarToCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    /// @brief Convert a contravariant vector to the transformed system
    GLOBAL_MAPPING_EXPORT void ContravarFromCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    /// @brief Convert a covariant vector to the transformed system
    GLOBAL_MAPPING_EXPORT void CovarFromCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    /**
     * @brief Get the Cartesian coordinates in the field
     *
     * This function is used to obtain the Cartesian coordinates
     * associated withthe Mapping
     *
     * @param out0  Coordinates in the x-direction
     * @param out1  Coordinates in the y-direction
     * @param out2  Coordinates in the z-direction
     */
    GLOBAL_MAPPING_EXPORT void GetCartesianCoordinates(
        Array<OneD, NekDouble> &out0, Array<OneD, NekDouble> &out1,
        Array<OneD, NekDouble> &out2)
    {
        v_GetCartesianCoordinates(out0, out1, out2);
    }
 
    /////////////////////////////////////////////////////////////
    //
    //   Basic tensor calculus functions
    //
    /////////////////////////////////////////////////////////////
 
    /**
     * @brief Get the Jacobian of the transformation
     *
     * This function is used to obtain the Jacobian of the Mapping.
     *
     * @param outarray Array containing the Jacobian
     */
    GLOBAL_MAPPING_EXPORT void GetJacobian(Array<OneD, NekDouble> &outarray)
    {
        v_GetJacobian(outarray);
    }
 
    /**
     * @brief Calculate the dot product with the gradient of the Jacobian
     *
     * This function calculates the dot product of an array against the
     * gradient of the Jacobian of the Mapping.
     *
     * @param inarray  Input array
     * @param outarray Output array
     */
    GLOBAL_MAPPING_EXPORT void DotGradJacobian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, NekDouble> &outarray)
    {
        v_DotGradJacobian(inarray, outarray);
    }
 
    /// @brief Get the metric tensor \f$g_{ij}\f$
    GLOBAL_MAPPING_EXPORT void GetMetricTensor(
        Array<OneD, Array<OneD, NekDouble>> &outarray)
    {
        v_GetMetricTensor(outarray);
    }
 
    /// @brief Get the inverse of metric tensor \f$g^{ij}\f$
    GLOBAL_MAPPING_EXPORT void GetInvMetricTensor(
        Array<OneD, Array<OneD, NekDouble>> &outarray)
    {
        v_GetInvMetricTensor(outarray);
    }
 
    /// @brief Lower index of vector: \f$v_{i} = g_{ij}*v^{j}\f$
    GLOBAL_MAPPING_EXPORT void LowerIndex(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    /// @brief Raise index of vector: \f$v^{i} = g^{ij}*v_{j}\f$
    GLOBAL_MAPPING_EXPORT void RaiseIndex(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    /**
     * @brief Apply the Christoffel symbols to a contravariant vector
     *
     * This function is used apply the Christoffel symbols
     * \f$ \left(  i,pk\right)\f$ to
     * a contravariant vector \f$u^p\f$, following the relation
     * \f[ (out)^{i}_{k} = \left(  i,pk\right)u^p \f]
     *
     * @param inarray  Contravariant vector \f$u^p\f$
     * @param outarray Result of applying Christoffel symbols to \f$u^p\f$
     */
    GLOBAL_MAPPING_EXPORT void ApplyChristoffelContravar(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray)
    {
        v_ApplyChristoffelContravar(inarray, outarray);
    }
 
    /**
     * @brief Apply the Christoffel symbols to a covariant vector
     *
     * This function is used apply the Christoffel symbols
     * \f$ \left(  p,ik\right)\f$ to
     * a covariant vector \f$u_p\f$, following the relation
     * \f[ (out)_{ik} = \left(  p,ik\right)u_p \f]
     *
     * @param inarray  Contravariant vector \f$u_p\f$
     * @param outarray Result of applying Christoffel symbols to \f$u_p\f$
     */
    GLOBAL_MAPPING_EXPORT void ApplyChristoffelCovar(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray)
    {
        v_ApplyChristoffelCovar(inarray, outarray);
    }
 
    /**
     * @brief Obtain the velocity of the coordinates
     *
     * This function is used to obtain the velocity of the coordinates
     * associated with the Mapping
     *
     * @param outarray  Velocity of the coordinates
     */
    GLOBAL_MAPPING_EXPORT void GetCoordVelocity(
        Array<OneD, Array<OneD, NekDouble>> &outarray)
    {
        v_GetCoordVelocity(outarray);
    }
 
    /////////////////////////////////////////////////////////////
    //
    //   Differential operators
    //
    /////////////////////////////////////////////////////////////
 
    /**
     * @brief Calculate the generalised divergence operator
     *
     * This function is used to calculate the generalised divergence
     * of a contravariant vector, defined as
     * \f[ D = u^i_{,i} = \frac{1}{J}\frac{\partial(Ju^i)}{\partial x^i}\f]
     *
     * @param inarray   Contravariant vector \f$u^i\f$
     * @param outarray  Divergence of \f$u^i\f$
     */
    GLOBAL_MAPPING_EXPORT void Divergence(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, NekDouble> &outarray)
    {
        v_Divergence(inarray, outarray);
    }
 
    /**
     * @brief Generalised (correction to the) velocity Laplacian operator
     *
     * This function is used to calculate a correction defined as
     * the difference between the generalised Laplacian and the
     * original Laplacian multiplied by a constant \f$\alpha\f$,
     *  resulting in
     * \f[ L^i = g^{jk}u^{i}_{,jk} - \alpha \frac{\partial^2 x^i}
     *           {\partial x^j \partial x^j}\f]
     * By default, \f$\alpha\f$ is zero, resulting in the generalised
     * Laplacian.
     *
     * @param inarray   Contravariant vector \f$u^i\f$
     * @param outarray  Result of the operation
     * @param alpha     The constant \f$\alpha\f$
     */
    GLOBAL_MAPPING_EXPORT void VelocityLaplacian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray,
        const NekDouble alpha = 0.0)
    {
        v_VelocityLaplacian(inarray, outarray, alpha);
    }
 
    /**
     * @brief Second order covariant derivatives of a contravariant vector
     *
     * This function computes the second order covariant derivatives
     * of a contravariant vector, resulting in \f$u^{i}_{,jk}\f$
     *
     * @param inarray   Contravariant vector \f$u^i\f$
     * @param outarray  Second order derivatives \f$u^{i}_{,jk}\f$
     */
    GLOBAL_MAPPING_EXPORT void gradgradU(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray)
    {
        v_gradgradU(inarray, outarray);
    }
 
    /**
     * @brief CurlCurl calculated on the whole field
     *
     * This function can be used to compute both the generalised CurlCurl
     * or the typical (Cartesian) CurlCurl, depending on the flag
     * generalized
     *
     * @param inarray      Contravariant vector \f$u^i\f$
     * @param outarray     CurlCurl of \f$u\f$
     * @param generalized  Flag defining if generalised or typical CurlCurl
     */
    GLOBAL_MAPPING_EXPORT void CurlCurlField(
        Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray, const bool generalized)
    {
        v_CurlCurlField(inarray, outarray, generalized);
    }
 
    /////////////////////////////////////////////////////////////
    //
    //   Functions defining mapping properties
    //
    /////////////////////////////////////////////////////////////
 
    /// @brief Get flag defining if mapping is time-dependent
    GLOBAL_MAPPING_EXPORT bool IsTimeDependent()
    {
        return m_timeDependent;
    }
 
    /// @brief Set flag defining if mapping is time-dependent
    GLOBAL_MAPPING_EXPORT void SetTimeDependent(const bool value)
    {
        m_timeDependent = value;
    }
 
    /// @brief Get flag defining if mapping is defined by a function
    GLOBAL_MAPPING_EXPORT bool IsFromFunction()
    {
        return m_fromFunction;
    }
 
    /// @brief Set flag defining if mapping is defined by a function
    GLOBAL_MAPPING_EXPORT void SetFromFunction(const bool value)
    {
        m_fromFunction = value;
    }
 
    /// @brief Get flag defining if mapping has constant Jacobian
    GLOBAL_MAPPING_EXPORT bool HasConstantJacobian()
    {
        return m_constantJacobian;
    }
 
    /// @brief Get flag determining if the mapping was defined or is trivial
    GLOBAL_MAPPING_EXPORT bool IsDefined()
    {
        return m_isDefined;
    }
 
    //
    //  Function to update time-dependent mappings
    //
 
    /// @brief Update the Dirichlet Boundary Conditions when using Mappings
    GLOBAL_MAPPING_EXPORT void UpdateBCs(const NekDouble time)
    {
        v_UpdateBCs(time);
    }
 
    /// @brief Update the Mapping with new coordinates
    GLOBAL_MAPPING_EXPORT void UpdateMapping(
        const NekDouble time,
        const Array<OneD, Array<OneD, NekDouble>> &coords =
            NullNekDoubleArrayOfArray,
        const Array<OneD, Array<OneD, NekDouble>> &coordsVel =
            NullNekDoubleArrayOfArray)
    {
        v_UpdateMapping(time, coords, coordsVel);
    }
 
    /// @brief Recompute the metric terms of the Mapping
    GLOBAL_MAPPING_EXPORT void UpdateGeomInfo()
    {
        v_UpdateGeomInfo();
    }
 
protected:
    /// Session reader
    LibUtilities::SessionReaderSharedPtr m_session;
    // FieldIO object used to output mapping
    LibUtilities::FieldIOSharedPtr m_fld;
    // Fields
    Array<OneD, MultiRegions::ExpListSharedPtr> m_fields;
    /// Array with the Cartesian coordinates
    Array<OneD, Array<OneD, NekDouble>> m_coords;
    /// Array with the velocity of the coordinates
    Array<OneD, Array<OneD, NekDouble>> m_coordsVel;
    /// Array with metric terms of the mapping
    Array<OneD, Array<OneD, NekDouble>> m_GeometricInfo;
    /// Number of velocity components
    int m_nConvectiveFields;
 
    /// Name of the function containing the coordinates
    std::string m_funcName;
    /// Name of the function containing the velocity of the coordinates
    std::string m_velFuncName;
 
    // Flags to help the solver
    /// Flag defining if the Jacobian is constant
    bool m_constantJacobian;
    /// Flag defining if the Mapping is time-dependent
    bool m_timeDependent;
    /// Flag defining if the Mapping is defined by a function
    bool m_fromFunction;
 
    // Static variables to load mapping
    static MappingSharedPtr m_mappingPtr;
    static bool m_init;
    static bool m_isDefined;
 
    // Workspace variables
    Array<OneD, Array<OneD, NekDouble>> m_wk1;
    Array<OneD, Array<OneD, NekDouble>> m_wk2;
    Array<OneD, Array<OneD, NekDouble>> m_tmp;
 
    /// @brief Constructor
    GLOBAL_MAPPING_EXPORT Mapping(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields);
 
    // Evaluators
    GLOBAL_MAPPING_EXPORT void EvaluateFunction(
        Array<OneD, MultiRegions::ExpListSharedPtr> pFields,
        LibUtilities::SessionReaderSharedPtr pSession, std::string pFieldName,
        Array<OneD, NekDouble> &pArray, const std::string &pFunctionName,
        NekDouble pTime = NekDouble(0));
 
    GLOBAL_MAPPING_EXPORT void EvaluateTimeFunction(
        LibUtilities::SessionReaderSharedPtr pSession, std::string pFieldName,
        Array<OneD, NekDouble> &pArray, const std::string &pFunctionName,
        NekDouble pTime = NekDouble(0));
 
    // Virtual functions
    GLOBAL_MAPPING_EXPORT virtual void v_InitObject(
        const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
        const TiXmlElement *pMapping);
 
    GLOBAL_MAPPING_EXPORT virtual void v_ContravarToCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_CovarToCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_ContravarFromCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_CovarFromCartesian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_GetCartesianCoordinates(
        Array<OneD, NekDouble> &out0, Array<OneD, NekDouble> &out1,
        Array<OneD, NekDouble> &out2);
 
    GLOBAL_MAPPING_EXPORT virtual void v_GetCoordVelocity(
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    GLOBAL_MAPPING_EXPORT virtual void v_GetJacobian(
        Array<OneD, NekDouble> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_DotGradJacobian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, NekDouble> &outarray);
 
    GLOBAL_MAPPING_EXPORT virtual void v_GetMetricTensor(
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_GetInvMetricTensor(
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_LowerIndex(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    GLOBAL_MAPPING_EXPORT virtual void v_RaiseIndex(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    GLOBAL_MAPPING_EXPORT virtual void v_ApplyChristoffelContravar(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_ApplyChristoffelCovar(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray) = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_Divergence(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, NekDouble> &outarray);
 
    GLOBAL_MAPPING_EXPORT virtual void v_VelocityLaplacian(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble alpha);
 
    GLOBAL_MAPPING_EXPORT virtual void v_gradgradU(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    GLOBAL_MAPPING_EXPORT virtual void v_CurlCurlField(
        Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray, const bool generalized);
 
    GLOBAL_MAPPING_EXPORT virtual void v_UpdateMapping(
        const NekDouble time,
        const Array<OneD, Array<OneD, NekDouble>> &coords =
            NullNekDoubleArrayOfArray,
        const Array<OneD, Array<OneD, NekDouble>> &coordsVel =
            NullNekDoubleArrayOfArray);
 
    GLOBAL_MAPPING_EXPORT virtual void v_UpdateGeomInfo() = 0;
 
    GLOBAL_MAPPING_EXPORT virtual void v_UpdateBCs(const NekDouble time);
};
 
} // namespace Nektar::GlobalMapping
 
#endif