Mastersthesis,
The Dirichlet--Neumann Iteration for Unsteady Thermal Fluid–Structure Interaction
Lund University, (2016)
Abstract
The efficient simulation of thermal interaction between fluids and structures is crucial in the design of many industrial products, e.g. turbine blades or rocket nozzles. The Dirichlet- Neumann iteration is one of the basic methods for simulating fluid structure interaction procedures.
In this thesis we analyze the convergence rate of the Dirichlet-Neumann iteration for the fully discretized unsteady transmission problem. Specifically, we consider the coupling of two linear heat equations on two identical non overlapping domains with jumps in the material coefficients across these as a model for thermal fluid structure interaction.
The implicit Euler method is used for the time discretization and
two different cases are considered with respect to the spatial
discretization. Firstly, both equations are discretized using a
finite element method. Secondly, finite volumes are employed on
one subdomain and finite elements on the other as usually done in
fluid structure interaction.
In this work, we provide an exact formula for the spectral radius of the iteration matrix in D and an estimate in D. We then show that these tend to the ratio of heat conductivities in the semidiscrete spatial limit, but to the ratio of the products of density and specific heat capacity in the semidiscrete temporal one. This explains the fast convergence previously
observed for cases with strong jumps in the material coefficients. Numerical results are presented to confirm the analysis
Tags
- 35k05-heat-equation
- 47j25-nonlinear-operators-iterative-procedures
- 65m55-pdes-ibvps-multigrid-methods-domain-decomposition
- 76r05-forced-convection
- conjugate-heat-transfer
