Dissipation-Based+Continuation

Dissipation-based continuation (DBC) is a scheme used to globalize the application of Newton's method for solving the Navier-Stokes equations for viscous flows or the Euler equations for inviscid flows. Jason Hicken first applied a DBC scheme to globalize the 3D Newton-Krylov flow solver DIABLO. Michal Osusky has since extended the implementation of DBC to handle viscous-turbulent flows in DIABLO. Click here for details of the DBC implementation in DIABLO. Howard Buckley has implemented DBC for inviscid flows in OPTIMA2D. Click here for details on the DBC implementation in OPTIMA2D.

The concept of DBC is to modify the non-linear problem using a dissipation-based operator such that the modified problem can easily be solved using Newton's method. The solution to the modified problem becomes the initial guess to a new modified problem where the influence from the dissipation-based operator is reduced. The DBC procedure continues in this way until the modified problem becomes the actual non-linear problem we want to solve. If we're lucky, the Newton-Krylov flow solver can proceed unassisted from this point until a converged solution is reached.