((((As a correction dissipation function in picture should have square of divergence of U)))) Hi, first of all I am aware that we have to discretize the non linear navier stokes equations to reach the almost exact solution, and pressure based or density based algorithms are deployed for that reason. But for the energy equation of navier stokes, dissipation function as in picture/attachment takes place and even if we apply finite difference or discretize the velocities we obtain square of those velocities and there is still a non linearity. But I know that pressure based or density based solvers should have linear algebraic matrix equations ( for instance pressure based algorithm uses segregated solution method which cares the linear algebraic system). MY QUESTİON is: How is the dissipation function treated especially for density based solver which include compressible flow ?? Dissipation function has non-linearity even if finite difference/discretization is applied so how do we handle this situation??