Help with numerical solution of parabolic equation
Hello? I have a task - to make a numerical solution of following equation: d2 H/ dr2 + 1/rd H/dr = S/T d H/dt . The first term is second derivative of H by r (polar coordinate), second term is first derivative of H by r multiple by 1/r and on the other site of Eq. there is first time derivative od H multiplied by term S/T. S is storativity, T is transmisivity. The equation is for radially symethric flow in confined aquifer, the analytic solution is by so called Well function (exponential integer) (Theis, 1935). It is an equation from groundwater flow and pumping test analysis. I need to make a numerical solution for a slug test with boundary and initial conditions for H(r,t): H(0,0) = H0, (the water level in the well is in one moment raised by H0 meters). The area is laterally infinite, the solution should be that the water level in well falls rapidly at first and then slowly... Can somebody help me with finding the best numerical method for modelling this process? I am lost a bit... Thanks
