Speaker
Description
Mesh-tying is a common computational approach for solving transport equations on two disjoint subdomains whose associated grids do not conform at the common interface. In the present contribution, we propose a finite volume adaptation of this general concept that is optimized for block-structured projection-based flow solvers. A characteristic trait of the method is that the interfacial mass fluxes and tractions are considered as unknown Lagrange multipliers whose values are determined such that the flow field remains continuous across the patched interface. With a view towards computational efficiency and implementational ease, the interfacial field of multipliers is spatially discretized by collocation at the face centers on one side of the interface. This choice is akin to the node-to-segment approach in computational contact mechanics and leads, in our formulation, to a weak satisfaction of the interfacial mass and momentum balances while ensuring continuity of the flow field at the collocation points. With the aid of an augmentation scheme, the multipliers are eliminated from the discrete system. By consequence, the system matrix's size is preserved and only a few additional non-zero entries are introduced. In a series of test cases ranging from the two-dimensional transport of a scalar in a disk-shaped domain to the Taylor-Couette flow and a rotor-driven fluid flow, we demonstrate that the proposed method maintains the optimal spatial accuracy order of the underlying flow solver on azimuthally equispaced but possibly non-conforming polar grids. The two-dimensional formulation extends immediately to three spatial dimensions if the grids are conforming but possibly non-uniform in the axial direction. In this regard, we present the application of the finite volume mesh-tying method to a three-dimensional baffled stirred tank.
