球状星团的 N 体模拟

问题描述

我正在尝试使用跳蛙方案编写 n 体模拟来模拟球状星团，但是我遇到了粒子从（我认为）接近其他粒子而被抛出系统的问题这导致势能的大幅增加。我曾尝试编写一些代码来解释碰撞，但如果我也使用软化因子，我不确定要使用什么碰撞半径。

初始位置在球体内随机生成，初始速度均为 0。

如果软化因子设置为 0.1 * 生成球体半径，碰撞半径设置为太阳半径（导致没有碰撞）与 N 个太阳质量的物体，我得到以下结果：

从能量图中，我们可以看到当物体最初彼此靠近时，势能会出现巨大的峰值。随着时间的推移，我的能量逐​​渐减少到 0，它认为只是由于数值计算。

有没有办法阻止这些星星被扔出去。我正在尝试调查初始集群需要多长时间才能形成平衡状态。

球体生成：

sun_mass = 1.989e30


N = 100
mass = sun_mass
M = np.full([N],mass)
R = 1e13
epsilon = 0.1 * R
collision_radius = 7e8
V = np.zeros([N,3])
M = np.full([N],mass)
P = np.zeros([N,3])


t = 50 * 365 * 24 * 60 * 60
dt = 30 * 24 * 60 * 60



print(t/dt)

np.random.seed(54321)

for i in range(N):
    
    phi = np.random.uniform(0,2*np.pi)
    costheta = np.random.uniform(-1,1)
    u = np.random.uniform(0,1)
    
    theta = np.arccos( costheta )
    r = R * (u) **(1/3)
    
    
    x = r * np.sin( theta) * np.cos( phi )
    y = r * np.sin( theta) * np.sin( phi )
    z = r * np.cos( theta )

    P[i] = (x,y,z)

程序：

def programe(position,mass,velocity,softening,time,dt,R,collision_radius):
    
    no_of_time_steps = (round(time/dt))

    all_positions = []
    all_velocities = []
    #print(all_positions)
    #print(len(all_positions[0]))
    kinetic_energy = []
    potential_energy = []
    total_energy = []
    
        
    for i in range(no_of_time_steps):
        
        position,velocity = detect_collisions(position,collision_radius)
        
        all_positions.append(position)
        all_velocities.append(velocity)
    
        'graph'
        plots = np.round(np.linspace(0,no_of_time_steps,num=500))
        for k in range(len(plots)):
            if i == plots[k]:
                print("test")
                #print(i)
                graph(position,k)
        
        'energies'
        kinetic_energy.append(calc_kinetic_energy(velocity,mass))
        potential_energy.append(calc_potential_energy(position,mass))
        total_energy.append(calc_total_energy(position,mass))
        
        'leap frog'
        velocity = calc_next_v_half(position,dt)    
        position = calc_next_position(position,dt)    
        velocity = calc_next_v_half(position,dt)
        

    
    all_positions = np.array(all_positions)
    graphing(all_positions,kinetic_energy,potential_energy,total_energy,R)
    #print(len(mass))

    return(all_positions,all_velocities,total_energy)

碰撞检测：

def indexOf(Array,item):
    for i in range(len(Array)):
        if (Array[i] == item).all():
            return i
        
def detect_collisions(position,collision_radius):
    i = 0
    
    newP = position
    newM = mass
    newV = velocity
    #print(len(position),len(newM))
    while i < len(newM):
        if newM[i] == 0:
            i += 1
            continue
        j = i + 1
        while j < len(newP):
           #print(j)
            if newM[j] == 0:
                j += 1
                continue
            p1 = position[i]
            p2 = position[j]
            
            if calc_seperation(p1,p2) < collision_radius:
                index1 = indexOf(position,p1)
                index2 = indexOf(position,p2)
                print('collision',index1,index2)
                newM,newV,newP = handle_collision(newM,newP,[index1,index2])
            j += 1
        i += 1
    
    return(newP,newM,newV)

def handle_collision(M,V,P,indexes):
    if M[indexes[0]] > M[indexes[1]]:
        primary = indexes[0]
        secondary = indexes[1]
    else:
        primary = indexes[1]
        secondary = indexes[0]

    primaryMomentum = M[primary] * V[primary]
    secondaryMomentum = M[secondary] * V[secondary]
    newMomentum = primaryMomentum + secondaryMomentum
    
    newMass = M[primary] + M[secondary]
    newVelocity = newMomentum / newMass
    M[primary] = newMass
    V[primary] = newVelocity
    M[secondary] = 0
    V[secondary] = 0
    P[secondary] = 0

    newM = np.delete(M,secondary,axis=0)
    newV = np.delete(V,axis=0)
    newP = np.delete(P,axis=0)

    return (newM,newP)
   

解决方法

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