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StateVector.h
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#pragma once
#include "IMEXRK.h"
// This class contains a full state's information
// its operations are not particularly efficient
// so it should only be used for high level algorithms
class StateVector
{
public:
StateVector()
{
Zero();
}
StateVector(const StateVector& other)
{
u1 = other.u1;
u2 = other.u2;
u3 = other.u3;
b = other.b;
EnforceBCs();
}
NeumannModal u1;
NeumannModal u2;
DirichletModal u3;
NeumannModal b;
NeumannModal p;
stratifloat FullEvolve(stratifloat T, StateVector& result, bool snapshot = false, bool screenshot = true, bool calcmixing = false) const;
void FixedEvolve(stratifloat deltaT, int steps, std::vector<StateVector>& result) const;
void LinearEvolve(stratifloat T, const StateVector& about, StateVector& result) const;
void AdjointEvolve(stratifloat deltaT, int steps, const std::vector<StateVector>& intermediate, StateVector& result) const;
const StateVector& operator+=(const StateVector& other)
{
u1 += other.u1;
if (gridParams.ThirdDimension())
{
u2 += other.u2;
}
u3 += other.u3;
b += other.b;
EnforceBCs();
return *this;
}
const StateVector& operator-=(const StateVector& other)
{
u1 -= other.u1;
if (gridParams.ThirdDimension())
{
u2 -= other.u2;
}
u3 -= other.u3;
b -= other.b;
EnforceBCs();
return *this;
}
const StateVector& MulAdd(stratifloat a, const StateVector& B)
{
u1 += a*B.u1;
if (gridParams.ThirdDimension())
{
u2 += a*B.u2;
}
u3 += a*B.u3;
b += a*B.b;
EnforceBCs();
return *this;
}
const StateVector& operator*=(stratifloat other)
{
u1 *= other;
if (gridParams.ThirdDimension())
{
u2 *= other;
}
u3 *= other;
b *= other;
EnforceBCs();
return *this;
}
const StateVector& operator=(const StateVector& other)
{
u1 = other.u1;
u2 = other.u2;
u3 = other.u3;
b = other.b;
EnforceBCs();
return *this;
}
stratifloat RemovePhaseShift()
{
stratifloat shift = -std::arg(u1(1,0,gridParams.N3/2))+pi/2;
return RemovePhaseShift(shift);
}
stratifloat RemovePhaseShift(stratifloat shift)
{
u1.PhaseShift(shift);
if (gridParams.ThirdDimension())
{
u2.PhaseShift(shift);
}
u3.PhaseShift(shift);
b.PhaseShift(shift);
return shift;
}
stratifloat Dot(const StateVector& other) const
{
stratifloat prod = InnerProd(u1, other.u1, flowParams.L3)
+ InnerProd(u3, other.u3, flowParams.L3)
+ flowParams.Ri*InnerProd(b, other.b, flowParams.L3); // TODO: is this correct PE?
if (gridParams.ThirdDimension())
{
prod += InnerProd(u2, other.u2, flowParams.L3);
}
return prod;
}
stratifloat Norm2() const
{
return Dot(*this);
}
stratifloat Energy() const
{
return 0.5*Norm2();
}
stratifloat Norm() const
{
return sqrt(Norm2());
}
stratifloat Enstrophy() const
{
DirichletModal FractionalTemp;
FractionalTemp = ddz(u1)+-1.0*ddx(u3);
return InnerProd(FractionalTemp, FractionalTemp, flowParams.L3);
}
stratifloat OtherAxis() const
{
NeumannModal pureSine;
for (int j=0; j<gridParams.N3; j++)
{
pureSine(1,0,j) = i;
}
return InnerProd(u3, pureSine, flowParams.L3);
}
stratifloat MinimumRi() const
{
solver.SetBackground(InitialU);
Neumann1D u_ave;
Neumann1D b_ave;
HorizontalAverage(u1, u_ave);
HorizontalAverage(b, b_ave);
u_ave = u_ave + solver.U_;
Neumann1D dbdz;
dbdz = ddz(b_ave);
Neumann1D dudz;
dudz = ddz(u_ave);
Neumann1D Ri_g;
for(int k=0; k<gridParams.N3; k++)
{
Ri_g.Get()[k] = flowParams.Ri*(dbdz.Get()[k]+1)/(dudz.Get()[k]*dudz.Get()[k]);
}
return Ri_g.Min();
}
void Zero()
{
u1.Zero();
if (gridParams.ThirdDimension())
{
u2.Zero();
}
u3.Zero();
b.Zero();
p.Zero();
}
void Rescale(stratifloat energy);
void ExciteLowWavenumbers(stratifloat energy);
void Randomise(stratifloat energy, bool restrictToMiddle = false)
{
u1.RandomizeCoefficients(0.3);
if (gridParams.ThirdDimension())
{
u2.RandomizeCoefficients(0.3);
}
u3.RandomizeCoefficients(0.3);
b.RandomizeCoefficients(0.3);
if (restrictToMiddle)
{
for (int j=0; j<gridParams.N3/4; j++)
{
u1.slice(j).setZero();
u1.slice(gridParams.N3-j-1).setZero();
u2.slice(j).setZero();
u2.slice(gridParams.N3-j-1).setZero();
u3.slice(j).setZero();
u3.slice(gridParams.N3-j-1).setZero();
b.slice(j).setZero();
b.slice(gridParams.N3-j-1).setZero();
}
}
Rescale(energy);
}
void LoadFromFile(const std::string& filename, bool twoDimensional = false)
{
std::string loadName = filename;
if (!EndsWith(loadName, ".fields"))
{
loadName += ".fields";
}
solver.LoadFlow(filename, twoDimensional);
CopyFromSolver();
}
void SaveToFile(const std::string& filename) const
{
CopyToSolver();
solver.PopulateNodalVariables();
if (EndsWith(filename, ".fields"))
{
solver.SaveFlow(filename);
}
else
{
solver.SaveFlow(filename+".fields");
}
}
template<int K1, int K2, int K3>
void LoadAndInterpolate(const std::string& filename)
{
// Set everything to zero. It interpolating to more modes, higher modes will not be overwritten
Zero();
// Load in to modal fields
NodalField<K1,K2,K3> U1Loaded(BoundaryCondition::Neumann);
NodalField<K1,K2,K3> U2Loaded(BoundaryCondition::Neumann);
NodalField<K1,K2,K3> U3Loaded(BoundaryCondition::Dirichlet);
NodalField<K1,K2,K3> BLoaded(BoundaryCondition::Neumann);
std::ifstream filestream(filename, std::ios::in | std::ios::binary);
U1Loaded.Load(filestream);
U2Loaded.Load(filestream);
U3Loaded.Load(filestream);
BLoaded.Load(filestream);
ModalField<K1,K2,K3> u1Loaded(BoundaryCondition::Neumann, gridParams.dimensionality==Dimensionality::ThreeDimensional);
ModalField<K1,K2,K3> u2Loaded(BoundaryCondition::Neumann, gridParams.dimensionality==Dimensionality::ThreeDimensional);
ModalField<K1,K2,K3> u3Loaded(BoundaryCondition::Dirichlet, gridParams.dimensionality==Dimensionality::ThreeDimensional);
ModalField<K1,K2,K3> bLoaded(BoundaryCondition::Neumann, gridParams.dimensionality==Dimensionality::ThreeDimensional);
U1Loaded.ToModal(u1Loaded);
U2Loaded.ToModal(u2Loaded);
U3Loaded.ToModal(u3Loaded);
BLoaded.ToModal(bLoaded);
// Vertical points to interpolate to/from
ArrayX oldNeumannPoints = VerticalPointsFractional(10, K3);
ArrayX oldDirichletPoints = VerticalPoints(10, K3);
ArrayX newNeumannPoints = VerticalPointsFractional(flowParams.L3, gridParams.N3);
ArrayX newDirichletPoints = VerticalPoints(flowParams.L3, gridParams.N3);
// just 2D for simplicity for now
assert(K2==1);
assert(gridParams.N2==1);
assert(!gridParams.ThirdDimension());
for (int j1=0; j1<std::min(K1/2+1,gridParams.N1/2+1); j1++)
{
// Neumann fields u1, u2 and b
for (int j3=0; j3<gridParams.N3; j3++)
{
stratifloat z = newNeumannPoints(j3);
// for each new gridpoint, find the old gridpoints either side
int k3_below;
int k3_above = 0;
stratifloat z_below;
stratifloat z_above;
do
{
k3_above++;
k3_below = k3_above-1;
z_below = oldNeumannPoints(k3_below);
z_above = oldNeumannPoints(k3_above);
} while(z_above<z && k3_above<K3-2);
// linearly interpolate between these points
stratifloat weight_above = (z-z_below)/(z_above-z_below);
stratifloat weight_below = (z_above-z)/(z_above-z_below);
if(weight_above > 1)
{
weight_above = 1;
weight_below = 0;
}
if (weight_below > 1)
{
weight_below = 1;
weight_above = 0;
}
u1(j1,0,j3) = weight_below*u1Loaded(j1,0,k3_below)
+ weight_above*u1Loaded(j1,0,k3_above);
u2(j1,0,j3) = weight_below*u2Loaded(j1,0,k3_below)
+ weight_above*u2Loaded(j1,0,k3_above);
b(j1,0,j3) = weight_below*bLoaded(j1,0,k3_below)
+ weight_above*bLoaded(j1,0,k3_above);
}
// neumann conditions
u1(j1,0,0) = u1(j1,0,1);
u2(j1,0,0) = u2(j1,0,1);
b(j1,0,0) = b(j1,0,1);
u1(j1,0,gridParams.N3-1)=u1(j1,0,gridParams.N3-2);
u2(j1,0,gridParams.N3-1)=u2(j1,0,gridParams.N3-2);
b(j1,0,gridParams.N3-1) = b(j1,0,gridParams.N3-2);
// same for dirichlet field u3
for (int j3=1; j3<gridParams.N3; j3++)
{
stratifloat z = newDirichletPoints(j3);
int k3_below;
int k3_above = 0;
stratifloat z_below;
stratifloat z_above;
do
{
k3_above++;
k3_below = k3_above-1;
z_below = oldDirichletPoints(k3_below);
z_above = oldDirichletPoints(k3_above);
} while(z_above<z && k3_above<K3-1);
stratifloat weight_above = (z-z_below)/(z_above-z_below);
stratifloat weight_below = (z_above-z)/(z_above-z_below);
if(weight_above > 1)
{
weight_above = 1;
weight_below = 0;
}
if (weight_below > 1)
{
weight_below = 1;
weight_above = 0;
}
u3(j1,0,j3) = weight_below*u3Loaded(j1,0,k3_below)
+ weight_above*u3Loaded(j1,0,k3_above);
}
}
EnforceBCs();
}
void EnforceBCs()
{
u3.ZeroEnds();
u1.NeumannEnds();
u2.NeumannEnds();
b.NeumannEnds();
}
void AddBackground()
{
NeumannNodal U1;
NeumannNodal B;
Neumann1D U_;
Neumann1D B_;
U_.SetValue(InitialU, flowParams.L3);
B_.SetValue([](stratifloat z){return z;}, flowParams.L3);
u1.ToNodal(U1);
b.ToNodal(B);
U1 += U_;
B += B_;
U1.ToModal(u1);
B.ToModal(b);
}
void RemoveBackground()
{
NeumannNodal U1;
NeumannNodal B;
Neumann1D U_;
Neumann1D B_;
U_.SetValue(InitialU, flowParams.L3);
B_.SetValue([](stratifloat z){return z;}, flowParams.L3);
u1.ToNodal(U1);
b.ToNodal(B);
U1 -= U_;
B -= B_;
U1.ToModal(u1);
B.ToModal(b);
}
void MakeMode2()
{
u1.MakeMode2();
u2.MakeMode2();
u3.MakeMode2();
b.MakeMode2();
}
void PlotAll(std::string directory) const
{
MakeCleanDir(directory);
HeatPlot(u1, flowParams.L1, flowParams.L3, 0, directory+"/u1.png");
if (gridParams.ThirdDimension())
{
HeatPlot(u2, flowParams.L1, flowParams.L3, 0, directory+"/u2.png");
}
HeatPlot(u3, flowParams.L1, flowParams.L3, 0, directory+"/u3.png");
HeatPlot(b, flowParams.L1, flowParams.L3, 0, directory+"/b.png");
DirichletModal FractionalTemp;
FractionalTemp = -1.0*ddz(u1)+ddx(u3);
HeatPlot(FractionalTemp, flowParams.L1, flowParams.L3, 0, directory+"/vorticity.png");
//HeatPlot(FractionalTemp, flowParams.L1, flowParams.L3, 0, directory+"/vorticity.eps");
if (gridParams.dimensionality == Dimensionality::TwoAndAHalf)
{
for (int n=0; n<gridParams.N2; n++)
{
HeatPlot(FractionalTemp, flowParams.L1, flowParams.L3, n, directory+"/vorticity"+std::to_string(n)+".png");
}
}
}
static void ResetForParams()
{
solver = IMEXRK();
}
private:
void CopyToSolver() const
{
solver.u1 = u1;
if (gridParams.ThirdDimension())
{
solver.u2 = u2;
}
else
{
solver.u2.Zero();
}
solver.u3 = u3;
solver.b = b;
solver.p = p;
}
void CopyFromSolver()
{
CopyFromSolver(*this);
}
void CopyFromSolver(StateVector& into) const
{
into.u1 = solver.u1;
if (gridParams.ThirdDimension())
{
into.u2 = solver.u2;
}
into.u3 = solver.u3;
into.b = solver.b;
into.p = solver.p;
into.EnforceBCs();
}
public:
static IMEXRK solver;
};
StateVector operator+(const StateVector& lhs, const StateVector& rhs);
StateVector operator-(const StateVector& lhs, const StateVector& rhs);
StateVector operator*(stratifloat scalar, const StateVector& vector);
StateVector operator*(const StateVector& vector, stratifloat scalar);