Error-Driven and Predictive Mesh Control for Adaptive Simulations of Incompressible Two-Phase Flows.

다국어 초록 (Multilingual Abstract)

A common bottleneck in simulation-based workflows is the control of the discretization error, which dictates the cost and accuracy of the simulation. Since the location and evolution of important solution features is unknown in advance for complex problems of interest, anadaptive approach becomes highly desirable. This is particularly the case for two-phase flows where interface evolution and dynamics are of interest.In this work, we present a robust, in-memory, and parallel mesh-adaptive workflow for incompressible two-phase flows that combines a two-phase flow solver with a posteriori error estimation and mesh adaptation including predictive mesh resolution. The error estimatoris derived from the variational multi-scale (VMS) paradigm and is then used to drive mesh adaptation. For problems with a highly dynamic interface, mesh adaptivity must be applied judiciously over time to control the computational cost, i.e., the rate or frequency of mesh adaptation must be controlled. Therefore, this work predictively defines the mesh resolution such that it is sufficient for a user-specified duration of time, where the trade-off is between the additional spread/width of regions with refined mesh resolution and the rate of mesh adaptation.These techniques are implemented and coupled with the Proteus toolkit, which includes an open-source multiphase flow solver. The overall implementation of the adaptive workflow is designed with parallel and large-scale applications in mind. To demonstrate its effectiveness, a number of complex two-phase flow cases are considered: a broad-crested weir case, a dam break case, and a 3D dam break case with an obstacle. Significant cost savings in computational time are shown for all three cases.