added md example

doc/examples.qbk

@@ -1,19 +1,27 @@
 
 [section Examples]
 
+[section Molecular Dynamics (Linear Spring) (MD)]
+
+Simple Molecular Dynamics of N particles interacting via a linear spring 
+potential. 
+
+[import ../tests/md.h]
+[md]
+[endsect]
+
 [section Brownian Dynamics (BD)]
 
 Brownian dynamics of N point particles around a set of spheres. The point 
 particles reflect off the spheres as they diffuse.
 
 [import ../tests/bd.h]
 [bd]
-
 [endsect]
 
-[section Molecular Dynamics (MD) / Discrete Element Model (DEM)] 
+[section Discrete Element Model (DEM)] 
 
-An Discrete Element Model example , simulating a polydisperse set of spherical 
+An Discrete Element Model example, simulating a polydisperse set of spherical 
 particles falling onto an surface.
 
 [import ../tests/dem.h]

tests/CMakeLists.txt

@@ -15,6 +15,7 @@ set(test_package
     dem
     sph
     bd
+    md
     )
 
 #set(test_package

tests/md.h

@@ -0,0 +1,167 @@
+/*
+ * md.h
+ *
+ *  Created on: 30 Jan 2014
+ *      Author: mrobins
+ */
+#ifndef MD_TEST_H_
+#define MD_TEST_H_
+
+#include <cxxtest/TestSuite.h>
+
+#define LOG_LEVEL 1
+//[md
+#include <random>
+typedef std::mt19937 generator_type;
+generator_type generator;
+
+#include "Aboria.h"
+using namespace Aboria;
+
+#include <boost/math/constants/constants.hpp>
+#include <math.h>
+
+//<-
+class MDTest : public CxxTest::TestSuite {
+public:
+
+    void test_md(void) {
+//->
+//=int main() {
+        const double PI = boost::math::constants::pi<double>();
+
+        /*
+         * Create a 2d particle container with one additional variable
+         * "velocity", represented by a 2d double vector
+         */
+        ABORIA_VARIABLE(velocity,double2,"velocity")
+        typedef Particles<std::tuple<velocity>,2> container_type;
+        typedef container_type::position position;
+        container_type particles;
+
+        /*
+         * set parameters for the MD simulation
+         */
+        const int timesteps = 3000;
+        const int nout = 200;
+        const int timesteps_per_out = timesteps/nout;
+        const double L = 31.0/1000.0;
+        const int N = 30;
+        const double diameter = 0.0022;
+        const double k = 1.0e01;
+        const double dens = 1160.0;
+        //const double mass = PI*std::pow(0.5*diameter,2)*dens;
+        const double mass = (1.0/6.0)*PI*std::pow(0.5*diameter,3)*dens;
+        const double reduced_mass = 0.5*mass;
+        const double dt = (1.0/50.0)*PI/sqrt(k/reduced_mass);
+        const double v0 = L/(timesteps*dt);
+
+        /*
+         * initiate neighbour search on a periodic 2d domain of side length L
+         */
+        particles.init_neighbour_search(double2(0,0),double2(L,L),diameter,bool2(true,true));
+
+        /*
+         * create N particles, ensuring that they do not overlap, according 
+         * to the set diameter. set the initial velocity in a random direction
+         */
+        std::uniform_real_distribution<double> uni(0,1);
+        for (int i = 0; i < N; ++i) {
+            bool free_position = false;
+
+            /*
+             * create new particle
+             */
+            container_type::value_type p;
+
+            /*
+             * set a random direction, and initialise velocity
+             */
+            const double theta = uni(generator)*2*PI;
+            get<velocity>(p) = v0*double2(cos(theta),sin(theta));
+
+            /*
+             * randomly choose positions within the domain until one is 
+             * found with no other particles within a range equal to diameter
+             */
+            while (free_position == false) {
+                get<position>(p) = double2(uni(generator)*L,uni(generator)*L);
+                free_position = true;
+
+                /*
+                 * loop over all neighbouring particles within a square with
+                 * side length "diameter" (see init_neighbour_search call above)
+                 */
+                for (auto tpl: particles.get_neighbours(get<position>(p))) {
+
+                    /*
+                     * tpl variable is a tuple containing:
+                     *  (0) -> neighbouring particle value_type
+                     *  (1) -> relative position of neighbouring particle
+                     *         from query point
+                     */
+                    const double2& dx = std::get<1>(tpl);
+                    const container_type::value_type& j = std::get<0>(tpl);
+                    if (dx.norm() < diameter) {
+                        free_position = false;
+                        break;
+                    }
+                }
+            }
+            particles.push_back(p);
+        }
+
+        /*
+         * create symbols and labels in order to use the expression API
+         */
+        Symbol<position> p;
+        Symbol<velocity> v;
+        Symbol<id> id_;
+        Label<0,container_type> a(particles);
+        Label<1,container_type> b(particles);
+
+        /*
+         * dx is a symbol representing the difference in positions of 
+         * particle a and b.
+         */
+        auto dx = create_dx(a,b);
+
+        /*
+         * sum is a symbolic function that sums a sequence of 2d vectors
+         */
+        Accumulate<std::plus<double2> > sum;
+
+        /*
+         * perform MD timestepping
+         */
+        for (int io = 0; io < nout; ++io) {
+
+            /*
+             * on every i/o step write particle container to a vtk
+             * unstructured grid file
+             */
+            std::cout << "." << std::flush;
+#ifdef HAVE_VTK
+            vtkWriteGrid("particles",io,particles.get_grid(true));
+#endif
+            for (int i = 0; i < timesteps_per_out; i++) {
+                /*
+                 * leap frog integrator
+                 */
+                v[a] += dt * ( 
+                        // spring force between particles
+                        sum(b, id_[a]!=id_[b] && norm(dx)<diameter, 
+                              -k*(diameter/norm(dx)-1)*dx)
+                        /mass
+                        );
+                p[a] += dt*v[a];
+            }
+        }
+        std::cout << std::endl;
+    }
+//]
+
+};
+
+#endif /* MD_TEST_H_ */
+