G exp(-alpha*(x^2+y^2)) Gaussian
p_i rho0*c0^2*G "Pressure initial condition"
u_i c0*beta*x*G "x-velocity initial condition"
v_i c0*beta*y*G "y-velocity initial condition"
dp_i "-c0^2*rho0*(d(u_i, x) + d(v_i, y))" "Time derivative of pressure initial condition"
r sqrt(x^2+y^2) "Distance variables"
p_a 1/(2*alpha)*integrate((cos(L*t)-beta/(2*alpha)*L*sin(L*t))*L*besselj(0,L*r)*exp(-L^2/(4*alpha)),L,0,10,1e-3) "Analytical pressure expression"