标题： 植被模型中多年冻土模块的相变热传导 显示英文标题

标题： Heat Conduction with Phase Change in Permafrost Modules of Vegetation Models

摘要： 我们研究了涉及相变的热传导问题，这对于地表模型和动态全球植被模型中的多年冻土建模至关重要。 这些模型需要最小的计算努力和极其健壮的大规模长期模拟求解器。 我们将Stefan问题的焓弱公式用作数学模型，并采用有限元法进行离散化。 利用非线性时间步方程组分段仿射结构的特点，我们证明该系统具有唯一解，并提供了一个保证从任意初始猜测在有限步内找到此解的求解器。 与Neumann解析解的比较以及在Lund-Potsdam-Jena管理的地表植被模型中的测试表明，新方法引入的计算成本并不比广泛使用的DECP方法显著更高，同时提供了更高的精度。 特别是，它避免了已知的解中的非物理伪影。 显示英文摘要

摘要： We consider the problem of heat conduction with phase change, that is essential for permafrost modeling in Land Surface Models and Dynamic Global Vegetation Models. These models require minimal computational effort and an extremely robust solver for large-scale, long-term simulations. The weak enthalpy formulation of the Stefan problem is used as the mathematical model and a finite element method is employed for the discretization. Leveraging the piecewise affine structure of the nonlinear time-stepping equation system, we demonstrate that this system has a unique solution and provide a solver that is guaranteed to find this solution in a finite number of steps from any initial guess. Comparisons with the Neumann analytical solution and tests in the Lund-Potsdam-Jena managed Land vegetation model reveal that the new method does not introduce significantly higher computational costs than the widely used DECP method while providing greater accuracy. In particular, it avoids a known nonphysical artifact in the solution.