In this paper we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the Finite Element Immersed Boundary Method (FE-IBM) to the actual Finite Element Distributed Lagrange Multiplier method (FE-DLM). We recall the well-posedness of our formulation at the continuous level in a simplified setting. We describe various time semi-discretizations that provide unconditionally stable schemes. Finally we report the stability analysis for the finite element space discretization where some improvements and generalizations of the previous results are obtained.
On the stability and conditioning of a fictitious domain formulation for fluid-structure interaction problems
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Dipartimento di Matematica ‘F. Casorati’, Università degli Studi di Pavia（帕维亚大学F. Casorati数学系）；Dipartimento di Ingegneria Civile, Architettura, Territorio, Ambiente e di Matematica, Università degli Studi di Brescia（布雷西亚大学土木、建筑、领土、环境及数学系）
Quadrature error estimates on non-matching grids in a fictitious domain framework for fluid-structure interaction problems
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Dipartimento di Matematica ‘F. Casorati’, Università degli Studi di Pavia（帕维亚大学 F. Casorati 数学系）；Istituto di Matematica Applicata e Tecnologie Informatiche ‘E. Magenes’, Consiglio Nazionale delle Ricerche（意大利国家研究委员会 E. Magenes 应用数学与信息技术研究所）；Dipartimento di Ingegneria Civile, Architettura, Territorio, Ambiente e di Matematica, Università degli Studi di Brescia（布雷西亚大学 土木、建筑、领土、环境与数学工程系）
A Unified-Field Monolithic Fictitious Domain-Finite Element Method for Fluid-Structure-Contact Interactions and Applications to Deterministic Lateral Displacement Problems
