Abstract
We present a new nonlinear algorithm for the efficient and accurate solution of isothermal and nonisothermal phase-change problems. The method correctly evolves latent heat release in isothermal and nonisothermal phase change, and more important, it provides a means for the efficient and accurate coupling between temperature and concentration fields in multispecies nonisothermal 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 outer Newton-based iteration and an inner conjugate gradient-like (Krylov) iteration. The effects of the Jacobian are probed only through approximate matrix-vector products required in the conjugate gradient-like iteration.
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