We consider single-phase flow with solute transport where ions in the fluid can precipitate and form a mineral, and where the mineral can dissolve and release solute into the fluid. Such a setting includes an evolving interface between fluid and mineral. We approximate the evolving interface with a diffuse interface, which is modeled with an Allen-Cahn equation. We also include effects from temperature such that the reaction rate can depend on temperature, and allow heat conduction through fluid and mineral. As Allen-Cahn is generally not conservative due to curvature-driven motion, we include a reformulation that is conservative. This reformulation includes a non-local term which makes the use of standard Newton iterations for solving the resulting non-linear system of equations very slow. We instead apply L-scheme iterations, which can be proven to converge for any starting guess, although giving only linear convergence. The three coupled equations for diffuse interface, solute transport and heat transport are solved via an iterative coupling scheme. This allows the three equations to be solved more efficiently compared to a monolithic scheme, and only few iterations are needed for high accuracy. Through numerical experiments we highlight the usefulness and efficiency of the suggested numerical scheme and the applicability of the resulting model.

翻译：我们考虑单相流中的溶质输运，其中流体中的离子能够沉淀形成矿物，同时矿物可溶解并将溶质释放回流体。此类场景包含流体与矿物之间随时间演化的界面。我们采用扩散界面近似该演化界面，并通过Allen-Cahn方程进行建模。此外，我们引入温度效应，使反应速率可依赖于温度，同时允许热量在流体与矿物间传导。由于Allen-Cahn方程因曲率驱动运动通常不具备保守性，我们纳入一种保守性重构形式。该重构包含非局部项，导致求解由此产生的非线性方程组时标准牛顿迭代极为缓慢。为此，我们采用L格式迭代，该方法虽仅具线性收敛性，但可证明对任意初始猜测均收敛。针对扩散界面、溶质输运与热输运的三个耦合方程，我们通过迭代耦合方案求解。相较于整体式方案，该方案能更高效地求解三个方程组，且仅需少量迭代即可获得高精度。数值实验凸显了所提数值方案的有效性与高效性，以及所得模型的适用性。