A Unified Momentum Equation Approach for Computing Flow-Induced Stresses in Structures with Arbitrarily-Shaped Stationary Boundaries (Communications in Computational Physics, 2019)
This article presents a novel monolithic numerical method for computingflow-induced stresses for problems involving arbitrarily-shaped stationary boundaries.A unified momentum equation for a continuum consisting of both fluids and solids isderived in terms of velocity by hybridizing the momentum equations of incompressible fluids and linear elastic solids. Discontinuities at the interface are smeared overa finite thickness around the interface using the signed distance function, and the resulting momentum equation implicitly takes care of the interfacial conditions withoutusing a body-fitted grid. A finite volume approach is employed to discretize the obtained governing equations on a Cartesian grid. For validation purposes, this methodhas been applied to three examples, lid-driven cavity flow in a square cavity, lid-drivencavity flow in a circular cavity, and flow over a cylinder, where velocity and stressfields are simultaneously obtained for both fluids and structures. The simulation results agree well with the results found in the literature and the results obtained byCOMSOL Multiphysics®.
Keywords: Flow induced stress; unified momentum equation; monolithic approach; smeared interface; stationary boundary.