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We present a new nonlinear algorithm for the e cient 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 importantly, it provides a means for the e cient and accurate coupling between temperature and concentration elds in multi-species nonisothermal phase change. The method rigorously conserves energy both globally and locally. Newton-like super-linear convergence isdoi:10.1080/104077999275839 fatcat:755eov2i5fgnlln3idcd55tjwm