The Finite Element Immersed Boundary Method with Distributed Lagrange Multiplier

2015/01/01 by Daniele Boffi, Nicola Cavallini, Lucia Gastaldi · 4 citations
Engineering · Mathematics · #Lattice Boltzmann Simulation Studies #Advanced Numerical Methods in Computational Mathematics #Gas Dynamics and Kinetic Theory

paper · doi:10.1137/140978399

Abstract

We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is unconditionally stable with respect to the time step size.

Cited by

• Splitting schemes for a Lagrange multiplier formulation of FSI with\n immersed thin-walled structure: stability and convergence analysis
• Augmented Lagrangian preconditioners for fictitious domain formulations of elliptic interface problems
• Low-Order Modeling and High-Fidelity Simulations for the Prediction of Combustion Instabilities in Liquid Rocket Engines and Gas Turbines
• A Fast, Accurate and Oscillation-free Spectral Collocation Solver for High-dimensional Transport Problems

Related

• The Finite Element Immersed Boundary Method with Distributed Lagrange multiplier
• A distributed Lagrange formulation of the Finite Element Immersed Boundary Method for fluids interacting with compressible solids
• Discrete models for fluid-structure interactions: the Finite Element Immersed Boundary Method
• On the stability and conditioning of a fictitious domain formulation for fluid-structure interaction problems
• Existence, uniqueness, and approximation of a fictitious domain formulation for fluid-structure interactions