我如何模拟二维球面波从一个点源

我试图通过使用欧拉积分对波动方程进行数值积分来模拟波动(直到我弄清楚这些问题，然后我将切换到龙格-库塔)。我使用浮点数数组作为网格。然后我通过改变网格在某一点上的值来制造一个扰动。现在，不是从这一点向四面八方辐射，波只向一个方向传播，向左上角，也就是向x和y递减，我的问题是如何让波向外辐射?

这是我的代码

void Wave::dudx(float *input,float *output) //calculate du/dx
{
    for(int y=0;y<this->height;y++)
    {
        for(int x=0;x<this->width;x++)
        {
            output[x+y*this->width]=(this->getPoint((x+1)%this->width,y)-this->getPoint(x,y)); //getPoint returns the value of the grid at (x,y)
        }
    }
}
void Wave::dudy(float *input,float *output) //calculate du/dy
{
    for(int x=0;x<this->width;x++)
    {
        for(int y=0;y<this->height;y++)
        {
            output[x+y*this->width]=(this->getPoint(x,(y+1)%this->height)-this->getPoint(x,y));
        }
    }
}
void Wave::simulate(float dt)
{
    float c=6.0f;
    //calculate the spatial derivatives
    this->dudx(this->points,this->buffer);
    this->dudx(this->buffer,this->d2udx2);
    this->dudy(this->points,this->buffer);
    this->dudy(this->buffer,this->d2udy2);
    for(int y=0;y<this->height;y++)
    {
        for(int x=0;x<this->width;x++)
        {
            this->points[x+y*this->width]+=c*c*(this->d2udx2[x+y*this->width]+this->d2udy2[x+y*this->width])*dt*dt; //I know that I can calculate c*c and dt*dt once, but I want to make it clear what I'm doing.
        }
    }
}