Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region.

We use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton’s method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. We show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Furthermore, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.

由于高温热源将多相流与能量传输耦合带来了重大的新挑战，因为沸腾和冷凝过程会导致干燥条件，随后再润湿。两相和单相行为之间的转变可能需要改变主要因变量，增加不连续性以及将本构非线性关系扩展到极端物理条件。大规模工程域的实际模拟导致雅可比系统具有大量未知数，必须在高性能计算机上并行使用迭代方法有效解决这些未知数。潜在核储存库的性能评估，碳封存场所和地热储层可能需要大量的蒙特卡罗模拟来探索材料特性、边界条件和失效场景的不确定性。由于数值挑战，标准 NR 迭代可能无法在所需模拟的范围内收敛，并且需要更复杂的优化方法，如信任区域。

我们使用开源模拟器 PFLOTRAN 解决美国能源部地质处置安全评估框架中未来核废料储存库安全评估的重要实际问题。该模拟器应用 PETSc 并行框架和反向欧拉有限体积离散化。我们证明了传统 NR 方法的失败和对牛顿方法的信任域修改的成功，用于解决一系列复杂性不断增加的测试问题。在标准 NR 迭代可能导致解发散或振荡的某些情况下，信任域方法本质上会修改牛顿步长和方向。我们展示了当多相状态因沸腾或冷凝而发生变化时，牛顿信任域方法如何适用于初级变量切换 (PVS)。高温热源的模拟导致了域中许多状态变化的极端非线性过程，并没有与 NR 收敛，但它们确实成功地完成了针对 PVS 修改的信任域方法。这种实施有效地将需要手动调整以完成模拟的数周模拟时间减少到一天。此外，我们展示了这些方法在 HPC 集群中的单个节点和多个节点上的强大可扩展性。