linearization
 

Hello, could anyone give me some tips on the following issue: linearization for the implicit time discretization of the following equation:

d(r)/dt + div(grad(phi)) = 0

with

r = r0 * ( 1 - (grad(phi))^2/(2*H0) )^(1/(gamma - 1))

t is time and r0 and H0 are reference (fixed) values. The non-linearity comes in with the dependence of r to phi, which is the independent variable. Thanks a lot for your help.

Debugged equation
 

Sorry there was an error, the actual equation is:

d(r)/dt + div( r * grad(phi) ) = 0

with

r = r0 * ( 1 - (grad(phi))^2/(2*H0) )^(1/(gamma - 1))