Discrete embedded boundary method with smooth dependence on the evolution of a fluid‐structure interface. (24th July 2020)

• Record Type: Journal Article
• Authors: Ho, Jonathan; Farhat, Charbel
• Other Names: van Brummelen E. Harald guestEditor.; Farhat Charbel guestEditor.
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 19(2021)
• Page Start: 5353
• Page End: 5383
• Publication Date: 2020-07-24
• Subjects: discrete events -- embedded boundary method -- FIVER -- fluid‐structure interaction -- immersed boundary method -- moving least squares -- radial basis functions; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6455
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: Embedded boundary methods (EBMs) are robust solution methods for highly nonlinear fluid‐structure interaction (FSI) problems. They suffer, however, some disadvantages because they perform their computations on embedding, nonbody‐fitted fluid meshes. In particular, they tend to generate discrete events that introduce discontinuities in the semi‐discretization process and lead to numerical solutions that are insufficiently smooth for differentiation with respect to the evolution of a discrete, fluid/structure interface Γ h F / S . This hinders their application to the gradient‐based solution of fluid‐structure optimization problems. Discrete events also promote spurious oscillations in the post‐processing of time‐dependent results computed at Γ h F / S .z This paper addresses these issues in the context of Finite Volume method with Exact two‐material Riemann problems (FIVER), a comprehensive framework for developing EBMs for highly nonlinear, compressible, FSI problems. It revisits the concept of the status of a node of an embedding fluid mesh and introduces that of a smoothness indicator nodal function, to eliminate discrete events and achieve smoothness in the semi‐discretization process. It also introduces a moving least squares approach in the loads evaluation algorithm, to suppress spurious oscillations from integral quantities computed on Γ h F / S . Equipped with these enhancements, FIVER is shown to deliver, for three different FSI applications, smooth results that are differentiable with respect to evolutions of Γ h F / S .