Physics simulation - fluid simulation
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using Plots, LinearAlgebra, Printf
# -----------------------------------------------------------------------------
# SPH Particle Data Structure
# -----------------------------------------------------------------------------
mutable struct Particle
position::Vector{Float64}
velocity::Vector{Float64}
acceleration::Vector{Float64}
density::Float64
pressure::Float64
mass::Float64
material::String
end
# -----------------------------------------------------------------------------
# Initialization
# -----------------------------------------------------------------------------
function initialize_particles()
particles = Vector{Particle}(undef, num_particles)
for i in 1:num_particles
pos = [rand() * box_size, rand() * box_size, rand() * 0.5] # Only bottom half
particles[i] = Particle(
pos,
[0.0, 0.0, 0.0], # velocity
[0.0, 0.0, -10.0], # acceleration
1000.0, # density
0.0, # pressure
1.0, # mass
"water" # material
)
end
return particles
end
# -----------------------------------------------------------------------------
# SPH Kernels
# -----------------------------------------------------------------------------
function kernel(r, h)
q = r / h
if q <= 1.0
return (1.0 - 1.5*q*q + 0.75*q*q*q) / (π * h^3)
elseif q <= 2.0
return 0.25 * (2.0 - q)^3 / (π * h^3)
else
return 0.0
end
end
# -----------------------------------------------------------------------------
# Density and Pressure Calculation
# -----------------------------------------------------------------------------
function calculate_density_pressure!(particles)
for i in 1:length(particles)
particles[i].density = 0.0
# Calculate density
for j in 1:length(particles)
r_vec = particles[i].position - particles[j].position
r = norm(r_vec)
particles[i].density += particles[j].mass * kernel(r, smoothing_length)
end
# Calculate pressure
particles[i].pressure = stiff_coef * ((particles[i].density/target_density)^7 - 1)
end
end
# -----------------------------------------------------------------------------
# Force Calculation
# -----------------------------------------------------------------------------
function calculate_forces!(particles)
for i in 1:length(particles)
grad_pressure = zeros(3)
laplacian_velocity = zeros(3)
# Calculate pressure gradient and velocity Laplacian
for j in 1:length(particles)
if i == j
continue
end
r_vec = particles[i].position - particles[j].position
r = norm(r_vec)
if r > smoothing_length || r == 0
continue
end
# Kernel gradient calculation
q = r / smoothing_length
kernel_grad = zeros(3)
if q <= 1.0
factor = (-3.0 + 2.25*q) / (π * smoothing_length^5)
kernel_grad = factor * r_vec
elseif q <= 2.0
factor = -0.75 * (2.0 - q)^2 / (π * smoothing_length^5 * q)
kernel_grad = factor * r_vec
end
# Pressure gradient (Equation 6)
pressure_term = (particles[i].pressure / (particles[i].density^2) +
particles[j].pressure / (particles[j].density^2))
grad_pressure += particles[j].mass * pressure_term * kernel_grad
# Velocity Laplacian (Equation 8)
v_ij = particles[i].velocity - particles[j].velocity
dot_r_grad = dot(r_vec, kernel_grad)
denominator = dot(r_vec, r_vec) + 0.01 * smoothing_length^2
if denominator != 0
laplacian_velocity += 2.0 * (particles[j].mass / particles[j].density) *
v_ij * (dot_r_grad / denominator)
end
end
# Pressure force (-∇P/ρ)
Fi_pressure = -grad_pressure
# Viscosity force (ν∇²v)
Fi_viscosity = particles[i].mass * viscosity_coef * laplacian_velocity
# Gravity
Fi_gravity = particles[i].mass * [0.0, 0.0, -10.0]
# Total forces
Fi = Fi_pressure + Fi_viscosity + Fi_gravity
# Update velocity and position
particles[i].velocity .+= (Fi / particles[i].mass) .* dt
particles[i].position .+= particles[i].velocity .* dt
@printf "Particle %d: Pos=(%.3f, %.3f, %.3f) Vel=(%.3f, %.3f, %.3f) Density=%.2f Pressure=%.2f Fi_pressure=(%.3f, %.3f, %.3f) Fi_viscosity=(%.3f, %.3f, %.3f)\n" i particles[i].position[1] particles[i].position[2] particles[i].position[3] particles[i].velocity[1] particles[i].velocity[2] particles[i].velocity[3] particles[i].density particles[i].pressure Fi_pressure[1] Fi_pressure[2] Fi_pressure[3] Fi_viscosity[1] Fi_viscosity[2] Fi_viscosity[3]
end
end
# -----------------------------------------------------------------------------
# Boundary Conditions
# -----------------------------------------------------------------------------
function apply_boundary_conditions!(particles)
for p in particles
# X boundaries
if p.position[1] < 0.0
p.position[1] = 0.0
p.velocity .*= -damping
elseif p.position[1] > box_size
p.position[1] = box_size
p.velocity .*= -damping
end
# Y boundaries
if p.position[2] < 0.0
p.position[2] = 0.0
p.velocity .*= -damping
elseif p.position[2] > box_size
p.position[2] = box_size
p.velocity .*= -damping
end
# Z boundaries
if p.position[3] < 0.0
p.position[3] = 0.0
p.velocity .*= -damping
elseif p.position[3] > box_size
p.position[3] = box_size
p.velocity .*= -damping
end
end
end
# -----------------------------------------------------------------------------
# Main Simulation Step
# -----------------------------------------------------------------------------
function simulate_step!(particles)
calculate_density_pressure!(particles)
calculate_forces!(particles)
apply_boundary_conditions!(particles)
end
# -----------------------------------------------------------------------------
# Visualization
# -----------------------------------------------------------------------------
function visualize_sph(particles, step)
x = [p.position[1] for p in particles]
y = [p.position[2] for p in particles]
z = [p.position[3] for p in particles]
plt = scatter3d(x, y, z,
markersize=3,
markercolor=:blue,
xlim=(0, box_size),
ylim=(0, box_size),
zlim=(0, box_size),
title="Time $(round(step, digits=2))s",
xlabel="X", ylabel="Y", zlabel="Z",
legend=false,
camera=(30, 60),
size=(400, 500)
)
return plt
end
# -----------------------------------------------------------------------------
# SPH Parameters
# -----------------------------------------------------------------------------
const num_particles = 1000
const dt = 0.01
const box_size = 1.0
const damping = 0.8
const smoothing_length = 0.1
const stiff_coef = 100.0
const target_density = 1000.0
const viscosity_coef = 0.2
# -----------------------------------------------------------------------------
# Main Simulation
# -----------------------------------------------------------------------------
function main()
particles = initialize_particles()
t = 0.0
frame_count = 0
while t < 10.0
simulate_step!(particles)
if frame_count % 1 == 0 # Save every frame
plt = visualize_sph(particles, t)
display(plt)
end
t += dt
frame_count += 1
end
end
main()
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