An efficient semi-implicit subgrid method for free-surface flows on hierarchical grids

• Published in: International journal for numerical methods in fluids 2016-04, Vol.80 (12), p.715-741
• Main Authors: Platzek, F. W., Stelling, G. S., Jankowski, J. A., Patzwahl, R., Pietrzak, J. D.
• Format: Article
• Language: English
• Subjects: Automation; Coarsening; Computational fluid dynamics; Convergence; efficiency; Fluid flow; grid convergence; hierarchical grids; Hydrodynamics; Mathematical models; shallow water; steady-state computations; Strategy; subgrid method
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4172

SUMMARY We present a new modelling strategy for improving the efficiency of computationally intensive flow problems in environmental free‐surface flows. The approach combines a recently developed semi‐implicit subgrid method with a hierarchical grid solution strategy. The method allows the incorporation of high‐resolution data on subgrid scale to obtain a more accurate and efficient hydrodynamic model. The subgrid method improves the efficiency of the hierarchical grid method by providing better solutions on coarse grids. The method is applicable to both steady and unsteady flows, but we particularly focus on river flows with steady boundary conditions. There, the combined hierarchical grid–subgrid method reduces the computational effort to obtain a steady state with factors up to 43. For unsteady models, the method can be used for efficiently generating accurate initial conditions on high‐resolution grids. Additionally, the method provides automatic insight in grid convergence. We demonstrate the efficiency and applicability of the method using a schematic test for the vortex shedding around a circular cylinder and a real‐world river case study. Copyright © 2015 John Wiley & Sons, Ltd. We present a semi‐implicit method for free surface flows that incorporates high‐resolution geometric data on subgrid level and applies a hierarchical grid solution strategy. The subgrid method makes sure that coarse‐grid solutions within the hierarchical grid approach resemble the fine‐grid solution, thereby considerably improving the efficiency and accuracy of the hydrodynamic model and providing automatic insight in grid convergence. A novel interpolation method that avoids the introduction of disturbances was applied to transfer data from coarse to fine grids.