This paper investigates numerical methods for simulations of the short-term behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There a given volume under or aside of a building is filled with soil and insulated to the surrounding ground. The thermal energy is stored by raising the temperature of the soil inside the storage. It is charged and discharged via pipe heat exchangers filled with a moving fluid. Simulations of geothermal energy storages aim to determine how much energy can be stored in or taken from the storage within a given short period of time. The latter depends on the dynamics of the spatial temperature distribution in the storage which is governed by a linear heat equation with convection and appropriate boundary and interface conditions. We consider semi- and full discretization of that PDE using finite difference schemes and study associated stability problems. Numerical results based on the derived methods are presented in the companion paper [17].

翻译：本文研究了模拟地热能存储短期行为的数值方法。此类模拟对于配备地下蓄热系统的住宅供暖系统的优化控制与管理至关重要。地下或建筑旁特定体积的空间填充土壤，并与周围地层隔热。热能通过提升蓄热体内土壤温度进行存储，并通过填充流动流体的管道换热器进行充放能。地热能存储模拟旨在确定给定短期时间内可从存储体储存或提取的能量。该能量取决于存储体内空间温度分布的动态特性，其由带有对流项及适当边界与界面条件的线性热方程控制。我们采用有限差分格式对该偏微分方程进行半离散化和全离散化，并研究相关的稳定性问题。基于所推导方法的数值结果见姊妹篇论文[17]。