import numpy from string import Template from simulation import Lattice, Geometry from utility.particles import Particles from utility.opengl import MomentsVertexBuffer from symbolic.generator import LBM import symbolic.D3Q27 as D3Q27 from OpenGL.GL import * from OpenGL.GLUT import * from OpenGL.GL import shaders from pyrr import matrix44, quaternion from geometry.sphere import Sphere from geometry.box import Box from geometry.cylinder import Cylinder lattice_x = 256 lattice_y = 64 lattice_z = 64 updates_per_frame = 10 particle_count = 100000 lid_speed = 0.02 relaxation_time = 0.51 def get_cavity_material_map(g): return [ (lambda x, y, z: x > 0 and x < g.size_x-1 and y > 0 and y < g.size_y-1 and z > 0 and z < g.size_z-1, 1), # bulk fluid (lambda x, y, z: x == 1 or x == g.size_x-2 or y == 1 or y == g.size_y-2 or z == 1 or z == g.size_z-2, 2), # walls (lambda x, y, z: x == 1, 3), # inflow (lambda x, y, z: x == g.size_x-2, 4), # outflow (Box(g.size_x//10, 1.5*g.size_x//10, 0, 2*g.size_y//5, 0, g.size_z), 5), (Box(g.size_x//10, 1.5*g.size_x//10, 3*g.size_y//5, g.size_y, 0, g.size_z), 5), (Sphere(g.size_x//3, g.size_y//2, g.size_z//2, 16), 5), (Cylinder(g.size_x//3, 0, g.size_z//2, 5, l = g.size_y), 5), (Cylinder(g.size_x//3, g.size_y//2, 0, 5, h = g.size_z), 5), (lambda x, y, z: x == 0 or x == g.size_x-1 or y == 0 or y == g.size_y-1 or z == 0 or z == g.size_z-1, 0) # ghost cells ] boundary = Template(""" if ( m == 2 || m == 5 ) { u_0 = 0.0; u_1 = 0.0; u_2 = 0.0; } if ( m == 3 ) { u_0 = min(time/5000.0 * $inflow, $inflow); u_1 = 0.0; u_2 = 0.0; } if ( m == 4 ) { rho = 1.0; } """).substitute({ "inflow": lid_speed }) def get_projection(width, height): world_width = lattice_x world_height = world_width / width * height projection = matrix44.create_perspective_projection(20.0, width/height, 0.1, 1000.0) look = matrix44.create_look_at( eye = [0, -2*lattice_x, 0], target = [0, 0, 0], up = [0, 0, -1]) point_size = 1 return numpy.matmul(look, projection), point_size class Rotation: def __init__(self, shift, x = numpy.pi, z = numpy.pi): self.shift = shift self.rotation_x = x self.rotation_z = z def update(self, x, z): self.rotation_x += x self.rotation_z += z def get(self): qx = quaternion.Quaternion(quaternion.create_from_eulers([self.rotation_x,0,0])) qz = quaternion.Quaternion(quaternion.create_from_eulers([0,0,self.rotation_z])) rotation = qz.cross(qx) return numpy.matmul( matrix44.create_from_translation(self.shift), matrix44.create_from_quaternion(rotation) ) def glut_window(fullscreen = False): glutInit(sys.argv) glutInitDisplayMode(GLUT_RGBA | GLUT_DOUBLE | GLUT_DEPTH) if fullscreen: window = glutEnterGameMode() else: glutInitWindowSize(800, 500) glutInitWindowPosition(0, 0) window = glutCreateWindow("LBM") return window lbm = LBM(D3Q27) window = glut_window(fullscreen = False) particle_shader = shaders.compileShader(""" #version 430 layout (location=0) in vec4 particles; out vec3 color; uniform mat4 projection; uniform mat4 rotation; vec3 fire(float x) { return mix( vec3(1.0, 1.0, 0.0), vec3(1.0, 0.0, 0.0), x ); } void main() { gl_Position = projection * rotation * vec4( particles[0], particles[1], particles[2], 1. ); color = fire(1.0-particles[3]); }""", GL_VERTEX_SHADER) vertex_shader = shaders.compileShader(Template(""" #version 430 layout (location=0) in vec4 vertex; out vec3 color; uniform mat4 projection; uniform mat4 rotation; void main() { gl_Position = projection * rotation * vertex; color = vec3(1.0,1.0,1.0); }""").substitute({}), GL_VERTEX_SHADER) lighting_vertex_shader = shaders.compileShader(""" #version 430 layout (location=0) in vec4 vertex; layout (location=2) in vec4 normal; out vec3 color; out vec3 frag_pos; out vec3 frag_normal; uniform mat4 projection; uniform mat4 rotation; void main() { gl_Position = projection * rotation * vertex; frag_pos = vertex.xyz; frag_normal = normalize(normal.xyz); color = vec3(0.6,0.6,0.6); }""", GL_VERTEX_SHADER) fragment_shader = shaders.compileShader(""" #version 430 in vec3 color; void main(){ gl_FragColor = vec4(color.xyz, 0.0); }""", GL_FRAGMENT_SHADER) lighting_fragment_shader = shaders.compileShader(Template(""" #version 430 in vec3 color; in vec3 frag_pos; in vec3 frag_normal; uniform mat4 projection; uniform mat4 rotation; out vec4 result; void main(){ const vec4 light_pos = rotation * vec4($size_x/2,-$size_x,$size_z/2,1); const vec3 light_color = vec3(1.0,1.0,1.0); const vec3 ray = light_pos.xyz - frag_pos; float brightness = dot(frag_normal, ray) / length(ray); brightness = clamp(brightness, 0, 1); result = vec4(max(0.4,brightness) * light_color * color.rgb, 1.0); } """).substitute({ "size_x": lattice_x, "size_y": lattice_y, "size_z": lattice_z }), GL_FRAGMENT_SHADER) particle_program = shaders.compileProgram(particle_shader, fragment_shader) projection_id = shaders.glGetUniformLocation(particle_program, 'projection') rotation_id = shaders.glGetUniformLocation(particle_program, 'rotation') domain_program = shaders.compileProgram(vertex_shader, fragment_shader) obstacle_program = shaders.compileProgram(lighting_vertex_shader, lighting_fragment_shader) lattice = Lattice( descriptor = D3Q27, geometry = Geometry(lattice_x, lattice_y, lattice_z), moments = lbm.moments(optimize = True), collide = lbm.bgk(f_eq = lbm.equilibrium(), tau = relaxation_time), boundary_src = boundary, opengl = True ) material_map = get_cavity_material_map(lattice.geometry) primitives = list(map(lambda material: material[0], filter(lambda material: not callable(material[0]), material_map))) lattice.apply_material_map(material_map) lattice.sync_material() moments_vbo = MomentsVertexBuffer(lattice) particles = Particles( lattice, moments_vbo, numpy.mgrid[ 2*lattice.geometry.size_x//100:4*lattice.geometry.size_x//100:particle_count/10000j, lattice.geometry.size_y//16:15*lattice.geometry.size_y//16:100j, lattice.geometry.size_z//16:15*lattice.geometry.size_z//16:100j, ].reshape(3,-1).T) rotation = Rotation([-lattice_x/2, -lattice_y/2, -lattice_z/2]) cube_vertices, cube_edges = lattice.geometry.wireframe() def on_display(): for i in range(0,updates_per_frame): lattice.evolve() moments_vbo.collect() for i in range(0,updates_per_frame): particles.update(aging = True) lattice.sync() glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT) glEnable(GL_DEPTH_TEST) glDepthFunc(GL_LESS) shaders.glUseProgram(particle_program) glUniformMatrix4fv(projection_id, 1, False, numpy.ascontiguousarray(projection)) glUniformMatrix4fv(rotation_id, 1, False, numpy.ascontiguousarray(rotation.get())) particles.bind() glEnable(GL_POINT_SMOOTH) glPointSize(point_size) glDrawArrays(GL_POINTS, 0, particles.count) shaders.glUseProgram(domain_program) glUniformMatrix4fv(projection_id, 1, False, numpy.ascontiguousarray(projection)) glUniformMatrix4fv(rotation_id, 1, False, numpy.ascontiguousarray(rotation.get())) glLineWidth(point_size) glBegin(GL_LINES) for i, j in cube_edges: glVertex(cube_vertices[i]) glVertex(cube_vertices[j]) glEnd() shaders.glUseProgram(obstacle_program) glUniformMatrix4fv(projection_id, 1, False, numpy.ascontiguousarray(projection)) glUniformMatrix4fv(rotation_id, 1, False, numpy.ascontiguousarray(rotation.get())) for primitive in primitives: primitive.draw() glutSwapBuffers() def on_reshape(width, height): global projection, point_size glViewport(0,0,width,height) projection, point_size = get_projection(width, height) def on_keyboard(key, x, y): global rotation x = { b'w': -numpy.pi/10, b's': numpy.pi/10 }.get(key, 0.0) z = { b'a': numpy.pi/10, b'd': -numpy.pi/10 }.get(key, 0.0) rotation.update(x,z) def on_timer(t): glutTimerFunc(t, on_timer, t) glutPostRedisplay() glutDisplayFunc(on_display) glutReshapeFunc(on_reshape) glutKeyboardFunc(on_keyboard) glutTimerFunc(10, on_timer, 10) glutMainLoop()