non linear continuity equation

S.Venkat

Hello,

I am working on a combustion problem in which i solve the continuity equation alongwith the species and the energy equations.(Pressure constant-low mach flow-momemtum eqn is not considered)The continuity equation is a nonlinear hyperbolic equation {rho=rho(r,t),v=v(r,t)}which has to be marched forward in radial direction to solve for radial velocity v,starting from an initially prescribed v. v is also to be used in the species and energy equations.I am unsure about the right approach to discretize and numerically implement this using the species and energy equations.Before solving for the continuity equation i discretize the species and energy equations and use the value of Y (mass fraction) and T in the equation of state to get an updated rho(n+1).I am not sure about handling the (rho*v) term which appears in the equation.I intend to linearize after discretizing the equation.I am using a crank nicholson scheme.Is this the sutable/appropriate approach.I would be grateful for any response

Thanks in advance

Venkat