Hydrodynamics Kernel
Jeffrey Oldham
oldham at codesourcery.com
Tue Apr 10 22:10:29 UTC 2001
One of the Pooma deliverables is a hydrodynamics kernel to test the
Field class and to use for timings. Attached is
1) the main hydrodynamics kernel file (also included in the archive)
2) a uuencoded gzipped tar archive with all the source files
To compile the program,
a. uudecode foo.uu # produces hydrodynamics.tgz
b. tar xzvf hydrodynamics.tgz # extracts the five files
c. In Makefile, modify the compiler definitions as necessary.
d. make # produces hydrodynamics
****************
There are several ways the code could be improved:
1) The two sequential portions of the code could be replaced by
data-parallel code. Modifying the initialization code should be
easy, but I do not know how to produce a data-parallel version of
the "product" operator.
2) Corner fields could be better supported. See my previously posted
proposal.
Please send suggestions, comments, and questions.
Thanks,
Jeffrey D. Oldham
oldham at codesourcery.com
-------------- next part --------------
// Oldham, Jeffrey D.
// 2001Mar27
// Pooma
// Hydrodynamics Kernel Written Using POOMA
#include <iostream>
#include <stdlib.h>
#include <cmath>
#include "Pooma/NewFields.h"
#include "ComputeVolumes.h"
#include "Product.h"
#include "ConstantVectorComponentBC.h"
// This hydrodynamics program implements "The Construction of
// Compatible Hydrodynamics Algorithms Utilizing Conservation of Total
// Energy," by E.J. Caramana, D.E. Burton, M.J. Shashkov, and
// P.P. Whalen, \emph{Journal of Computational Physics}, vol. 146
// (1998), pp. 227-262.
// The code uses fields with two different granularities: coarse and
// fine. Both grid conceptually cover the same domain, but the
// fine-grain one has twice the number of values for each dimension.
// Currently, Pooma does not nicely support operations between fields
// with different granularities. The code occurring between
// `CORNER_FIELD_TEMPORARY' preprocessor values substitutes for this
// lack of support. See the separately distributed proposal for
// details.
// Preprocessor symbols:
// CORNER_FIELD_TEMPORARY: Define this symbol. Include code to deal
// with different granularity fields.
// PSEUDOCODE: Do not define this symbol. Surrounds desired code to
// deal with different granularity fields.
// DEBUG: If defined, print some information about internal program
// values.
// DEBUG2: If defined, print much more information about internal
// program values.
// Sample compilation command:
// g++ -g -DCORNER_FIELD_TEMPORARY -I/nfs/oz/home/oldham/pooma/r2/src/ -I/nfs/oz/home/oldham/pooma/r2/lib/LINUXgcc/ -L. hydrodynamics.cc -lpooma-gcc -o hydrodynamics
#ifdef CORNER_FIELD_TEMPORARY
/** FORWARD DECLARATIONS **/
template<class InputGeometry, class OutputGeometry, class T, class EngineTag>
inline
void
sumAroundCell (const Field<InputGeometry, T, EngineTag> & input,
Field<OutputGeometry, T, EngineTag> & output);
template<class InputGeometry, class OutputGeometry, class T, class EngineTag>
inline
void
sumAroundVertex(const Field<InputGeometry, T, EngineTag> & input,
Field<OutputGeometry, T, EngineTag> & output);
template<class InputGeometry1,
class InputT1, class InputT2,
class InputEngineTag1, class InputEngineTag2,
class OutputGeometry, class OutputT, class OutputEngineTag>
inline
void
computeCornerMasses(const Field<InputGeometry1, InputT1, InputEngineTag1> & pressureDensity,
const Field<OutputGeometry, InputT2, InputEngineTag2> & fineCoordinates,
Field<OutputGeometry, OutputT, OutputEngineTag> & output);
template <class InputGeometry1,
class InputT1, class InputT2,
class InputEngineTag1, class InputEngineTag2,
class OutputGeometry, class OutputT, class OutputEngineTag>
inline
void
computeCornerForces(const Field<InputGeometry1, InputT1, InputEngineTag1> & pressure,
const Field<OutputGeometry, InputT2, InputEngineTag2> & coordinates,
Field<OutputGeometry, OutputT, OutputEngineTag> & output);
template <class InputGeometry1,
class InputT1,
class InputEngineTag1,
class OutputGeometry, class OutputT, class OutputEngineTag>
inline
void
copyVelocities(const Field<InputGeometry1, InputT1, InputEngineTag1> & input1,
const Field<InputGeometry1, InputT1, InputEngineTag1> & input2,
Field<OutputGeometry, OutputT, OutputEngineTag> & output);
#endif // CORNER_FIELD_TEMPORARY
/** THE HYDRODYNAMICS PROGRAM **/
int main(int argc, char *argv[])
{
// Set up the Pooma library.
Pooma::initialize(argc,argv);
#ifdef DEBUG
std::cout << "Hello, world." << std::endl;
#endif // DEBUG
/* DECLARATIONS */
// Values
const double gamma = 4.0/3; // gas pressure constant $\gamma$
const double timeStep = 0.01; // $\Delta t$
unsigned nuIterations = 1; // number of iterations
// Create a simple layout.
const unsigned Dim = 2; // Work in a 2D world.
const unsigned nHorizVerts = 11; // number of horizontal vertices
const unsigned nAngles = 5; // number of angles
Interval<Dim> vertexDomain;
vertexDomain[0] = Interval<1>(nHorizVerts);
vertexDomain[1] = Interval<1>(nAngles);
DomainLayout<Dim> layout(vertexDomain, GuardLayers<2>(1));
// Preparation for Field creation.
Vector<Dim> origin(0.0);
Vector<Dim> spacings(1.0,1.0); // TODO: What does this do?
typedef UniformRectilinear<Dim, double, Cartesian<Dim> > Geometry_t;
typedef Field<Geometry_t, double, Brick> Fields_t;
typedef Field<Geometry_t, double, Brick> ConstFields_t; // TODO: Change to ConstField when ConstField is available.
typedef Field<Geometry_t, Vector<Dim>, Brick> Fieldv_t;
typedef Field<Geometry_t, Vector<Dim>, Brick> ConstFieldv_t; // TODO: Change to ConstField when ConstField is available.
// Cell-centered Fields.
Cell cell;
Fields_t internalEnergy (cell, layout, origin, spacings);
ConstFields_t zoneMass (cell, layout, origin, spacings);
Fields_t pressure (cell, layout, origin, spacings);
Fields_t pressureDensity (cell, layout, origin, spacings);
Fields_t volume (cell, layout, origin, spacings);
// Vertex-centered Fields.
Vert vert;
ConstFields_t pointMass (vert, layout, origin, spacings);
Fieldv_t coordinates (vert, layout, origin, spacings);
Fieldv_t velocity (vert, layout, origin, spacings);
Fieldv_t velocityChange (vert, layout, origin, spacings);
// Corner Fields.
// TODO: How should I implement corner Fields?
#ifdef CORNER_FIELD_TEMPORARY
// For now, implement corner Fields using a Field with twice as many
// entries in each dimension.
Interval<Dim> cornerVertexDomain;
for (unsigned d = 0; d < Dim; ++d)
cornerVertexDomain[d] = Interval<1>(2*vertexDomain[d].min(),2*vertexDomain[d].max());
DomainLayout<Dim> cornerLayout(cornerVertexDomain, GuardLayers<2>(1));
Fieldv_t cornerForces (cell, cornerLayout, origin, spacings);
Fields_t cornerMasses (cell, cornerLayout, origin, spacings);
Fieldv_t cornerCoordinates(vert, cornerLayout, origin, spacings);
Fieldv_t cornerVelocities(vert, cornerLayout, origin, spacings);
Fields_t tmp1 (cell, cornerLayout, origin, spacings);
Fields_t tmp2 (cell, cornerLayout, origin, spacings);
#endif // CORNER_FIELD_TEMPORARY
/* INITIALIZATION */
// TODO: Is coordinates initialization necessary? What is the best way to do this?
for (unsigned xIndex = 0; xIndex <= vertexDomain[0].last (); ++xIndex)
for (unsigned yIndex = 0; yIndex <= vertexDomain[1].last (); ++yIndex)
coordinates(xIndex,yIndex) =
Vector<2>(static_cast<double>(xIndex)/(nHorizVerts-1) * cos(yIndex*M_PI/(2*(nAngles-1))),
static_cast<double>(xIndex)/(nHorizVerts-1) * sin(yIndex*M_PI/(2*(nAngles-1))));
for (unsigned xIndex = 0; xIndex <= cornerVertexDomain[0].last (); ++xIndex)
for (unsigned yIndex = 0; yIndex <= cornerVertexDomain[1].last (); ++yIndex)
cornerCoordinates(xIndex,yIndex) =
Vector<2>(0.5*xIndex/(nHorizVerts-1) * cos(0.5*yIndex*M_PI/(2*(nAngles-1))),
0.5*xIndex/(nHorizVerts-1) * sin(0.5*yIndex*M_PI/(2*(nAngles-1))));
#ifdef DEBUG
std::cout << "initial coordinates:\n" << coordinates << std::endl;
#endif // DEBUG
internalEnergy = 1.0;
pressureDensity = 1.0;
#ifdef PSEUDOCODE
// This is the desired code:
cornerMasses = replicate<2>(pressureDensity) *
computeVolumes(interpolate<2>(coordinates));
pointMass = total<2>(cornerMasses);
zoneMass = total<2>(cornerMasses);
// This is the code that Pooma currently supports:
#endif // PSEUDOCODE
#ifdef CORNER_FIELD_TEMPORARY
computeCornerMasses(pressureDensity, cornerCoordinates, cornerMasses);
sumAroundVertex(cornerMasses, pointMass);
sumAroundCell(cornerMasses, zoneMass);
#endif // CORNER_FIELD_TEMPORARY
PInsist(min(pointMass) > 0.0, "Zero masses are not supported.");
#ifdef DEBUG2
std::cout << "pointMass:\n" << pointMass << std::endl;
std::cout << "zoneMass:\n" << zoneMass << std::endl;
#endif // DEBUG2
velocity = Vector<Dim>(0.0);
velocityChange.addUpdaters(AllConstantFaceBC<Vector<Dim> >(Vector<Dim>(0.0), false));
for (int d = 0; d < Dim; ++d)
velocityChange.addUpdater(ConstantVectorComponentBC<Vector<Dim>::Element_t>(2*d, d, 0.0, true));
velocityChange.addUpdater(ConstantVectorComponentBC<Vector<Dim>::Element_t>(3, 0, 0.0, true));
/* ITERATIONS */
for (; nuIterations > 0; --nuIterations) {
#ifdef DEBUG
std::cout << "Begin an iteration." << std::endl;
#endif // DEBUG
pressure = (gamma - 1.0) * pressureDensity * internalEnergy;
#ifdef DEBUG2
std::cout << "pressure:\n" << pressure << std::endl;
#endif // DEBUG2
#ifdef PSEUDOCODE
// This is the desired code.
forces = replicate<2>(pressure) * addNormals(coordinates);
velocityChange = (timeStep / pointMass) * total<2>(cornerForces);
// This is the code that Pooma currently supports:
#endif // PSEUDOCODE
#ifdef CORNER_FIELD_TEMPORARY
computeCornerForces(pressure, coordinates, cornerForces);
sumAroundVertex(cornerForces, velocityChange);
velocityChange *= timeStep / pointMass;
#endif // CORNER_FIELD_TEMPORARY
#ifdef DEBUG2
std::cout << "corner forces:\n" << cornerForces << std::endl;
std::cout << "velocity changes:\n" << velocityChange << std::endl;
#endif // DEBUG2
velocityChange.update();
#ifdef PSEUDOCODE
// This is the desired code.
internalEnergy +=
-(timeStep / pointMass) *
total<2>(dot(cornerForces, replicate<2>(velocity + 0.5*velocityChange)));
// This is the code that Pooma currently supports:
#endif // PSEUDOCODE
#ifdef CORNER_FIELD_TEMPORARY
copyVelocities(velocity, velocityChange, cornerVelocities);
tmp1 = dot(cornerForces, cornerVelocities);
sumAroundCell(tmp1, tmp2);
internalEnergy += -(timeStep / pointMass) * tmp2;
#endif // CORNER_FIELD_TEMPORARY
coordinates += (velocity + 0.5*velocityChange) * timeStep;
velocity += velocityChange;
volume = computeVolumes(coordinates);
pressureDensity = zoneMass / volume;
#ifdef DEBUG2
std::cout << "pressure density:\n" << pressureDensity << std::endl;
#endif // DEBUG2
}
/* TERMINATION */
std::cout << "final coordinates:\n" << coordinates << std::endl;
#ifdef DEBUG
std::cout << "Goodbye, world." << std::endl;
#endif // DEBUG
Pooma::finalize();
return EXIT_SUCCESS;
}
/** HELPER FUNCTIONS **/
#ifdef CORNER_FIELD_TEMPORARY
// Following is temporary code to permit compilation using the current
// Pooma code. Adding new Pooma abstractions may eliminate the need
// for this code.
static Loc<2> offset[] = { Loc<2>(0,0), Loc<2>(0,1),
Loc<2>(1,0), Loc<2>(1,1) };
// Given a Field with twice the refinement, form a cell-centered Field
// by summing the 1<<Dim corresponding corners.
template<class InputGeometry, class OutputGeometry, class T, class EngineTag>
inline
void
sumAroundCell(const Field<InputGeometry, T, EngineTag> & input,
Field<OutputGeometry, T, EngineTag> & output)
{
const int dim = Field<OutputGeometry, T, EngineTag>::dimensions;
Field<OutputGeometry,T,EngineTag>::Domain_t range = output.physicalDomain();
output(range) = 0;
for (unsigned counter = 0; counter < (1<<dim); ++counter)
output(range) += input(2*range+offset[counter]);
return;
}
// Given a Field with twice the refinement, form a vertex-centered Field
// by summing the 1<<Dim corresponding corners.
template<class InputGeometry, class OutputGeometry, class T, class EngineTag>
inline
void
sumAroundVertex(const Field<InputGeometry, T, EngineTag> & input,
Field<OutputGeometry, T, EngineTag> & output)
{
const int dim = Field<OutputGeometry, T, EngineTag>::dimensions;
Field<OutputGeometry,T,EngineTag>::Domain_t range = output.physicalDomain();
output(range) = 0;
for (unsigned counter = 0; counter < (1<<dim); ++counter)
output(range) += input(2*range-offset[counter]);
return;
}
// Given a quadrilateral's two diagonals as vectors, return the
// quadrilateral's volume.
template <int Dim, class T, class E>
inline
double
quadrilateralVolume (const Vector<Dim,T,E> &v, const Vector<Dim,T,E> &w)
{
return 0.5 * std::abs (sum (product (v, w)));
}
// Given a pressure density Field and a fine-mesh coordinate Field, compute
// corner masses, placing in "output".
// TODO: Extend to multiple dimensions.
template<class InputGeometry1,
class InputT1, class InputT2,
class InputEngineTag1, class InputEngineTag2,
class OutputGeometry, class OutputT, class OutputEngineTag>
inline
void
computeCornerMasses(const Field<InputGeometry1, InputT1, InputEngineTag1> & pressureDensity,
const Field<OutputGeometry, InputT2, InputEngineTag2> & fineCoordinates,
Field<OutputGeometry, OutputT, OutputEngineTag> & output)
{
// Assume the temporary finer coordinates Field fineCoordinates
// already has values.
// Compute the volumes in fineCoordinates.
output = computeVolumes(fineCoordinates);
// Multiply each volume by the pressure density.
Field<InputGeometry1,InputT1,InputEngineTag1>::Domain_t range = pressureDensity.physicalDomain();
const unsigned corners =
(1 << (Field<InputGeometry1, InputT1, InputEngineTag1>::dimensions));;
for (unsigned c = 0; c < corners; ++c)
output(2*range+offset[c]) *= pressureDensity(range);
return;
}
// Given a pressure Field and a coordinate Field, compute the corner
// forces in a fine-mesh Field.
template <class InputGeometry1,
class InputT1, class InputT2,
class InputEngineTag1, class InputEngineTag2,
class OutputGeometry, class OutputT, class OutputEngineTag>
inline
void
computeCornerForces(const Field<InputGeometry1, InputT1, InputEngineTag1> & pressure,
const Field<OutputGeometry, InputT2, InputEngineTag2> & coordinates,
Field<OutputGeometry, OutputT, OutputEngineTag> & output)
{
Field<InputGeometry1,InputT1,InputEngineTag1>::Domain_t range = pressure.physicalDomain();
for (unsigned xIndex = 0; xIndex <= range.unwrap()[0].last(); ++xIndex)
for (unsigned yIndex = 0; yIndex <= range.unwrap()[1].last(); ++yIndex) {
Loc<2> range (xIndex, yIndex);
output(2*range + offset[0]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[2])
- coordinates(range+offset[1]));
output(2*range+offset[1]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[0])
- coordinates(range+offset[3]));
output(2*range+offset[2]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[3])
- coordinates(range+offset[0]));
output(2*range+offset[3]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[1])
- coordinates(range+offset[2]));
}
return;
#ifdef PSEUDOCODE
// TODO: I really wanted to use "range" in a data-parallel
// statement, but I do not know how to extend "product" to work
// on Fields for such a statement.
Field<InputGeometry1,InputT1,InputEngineTag1>::Domain_t range = pressure.physicalDomain();
output(2*range+offset[0]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[2])
- coordinates(range+offset[1]));
output(2*range+offset[1]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[0])
- coordinates(range+offset[3]));
output(2*range+offset[2]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[3])
- coordinates(range+offset[0]));
output(2*range+offset[3]) =
pressure(range) *
0.5 * product(InputT2(1.0),
coordinates(range+offset[1])
- coordinates(range+offset[2]));
#endif // PSEUDOCODE
}
template <class InputGeometry, class InputT, class InputEngineTag,
class OutputGeometry, class OutputT, class OutputEngineTag>
inline
void
copyVelocities(const Field<InputGeometry, InputT, InputEngineTag> & input1,
const Field<InputGeometry, InputT, InputEngineTag> & input2,
Field<OutputGeometry, OutputT, OutputEngineTag> & output)
{
Field<InputGeometry,InputT,InputEngineTag>::Domain_t range =
input1.physicalDomain();
output(2*range-offset[0]) =
output(2*range-offset[1]) =
output(2*range-offset[2]) =
output(2*range-offset[3]) = input1(range) + 0.5*input2(range);
return;
}
#endif // CORNER_FIELD_TEMPORARY
-------------- next part --------------
begin 660 hydrodynamics.tgz
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`
end
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