A new nonlinear solution method for phase-change problems

We present a new nonlinear algorithm for the efficient and accurate solutio n of isothermal and nonisothermal phase-change problems. The method correct ly evolves latent heat release in isothermal and nonisothermal phase change , and more important, it provides a means for the efficient and accurate co upling between temperature and concentration fields in multispecies nonisot hermal phase change. Newton-like superlinear convergence is achieved in the global nonlinear iteration, without the complexity of forming or inverting the Jacobian matrix. This "Jacobian-free" method is a combination of an ou ter Newton-based iteration and an inner conjugate gradient-like (Krylov) it eration. The effects of the Jacobian are probed only through approximate ma trix-vector products required in the conjugate gradient-like iteration.