10.4122/1.1000000750
Janssen, Hans
Hans
Janssen
hans.janssen@bwk.kuleuven.be
Carmeliet, Jan
Jan
Carmeliet
jan.carmeliet@bwk.kuleuven.be
Janssen, Hans
Hans
Janssen
hans.janssen@bwk.kuleuven.be
Adaptive integration of element matrices in finite-element moisture transfer simulations
XVI International Conference on Computational Methods in Water Resources
2006
2006
While serving different purposes, numerical simulations of moisture and heat
transfer
in soils and in building components are very similar in methodology: in both cases,
spatially and temporally discretised equations for transfer of moisture and heat in
porous materials are solved subject to (atmospheric) boundary conditions. The
strongly non-linear transfer equations and boundary conditions however render such
hygrothermal simulations computationally very expensive, and an efficient numerical
solution algorithm is required. Such increasingly efficient numerical solution
schemes allow for more, larger, longer or more precise simulations, widening the
application capabilities of hygrothermal simulations.
The computational cost of hygrothermal simulations revolves around the serial
iterative com-position and decomposition of the coefficient matrix of the system of
algebraic equations de-scribing the discretised moisture and heat transfer, and is
thus determined by the cost of one (de)composition, and the number of required
(de)compositions. This article presents two op-timisation measures for simulations
of moisture and heat transfer in building components un-der atmospherical
excitation:
adaptive integration and variations on the Newton-Raphson iterative scheme.
Adaptive
integration targets the cost of one (de)composition, while the varia-tions on
Newton-Raphson aims at the number of required (de)compositions. While exempli-fied
by building physical simulations, the presented optimisation measures are equally
valid for simulations of moisture and heat transfer in soils.
It will be demonstrated that the common preference for low-order numerical
integration of the finite element matrices has an adverse effect on the required
spatial discretisation: a fine dis-cretisation throughout is needed for accurate
simulation of the moving moisture fronts typical of infiltration problems. Adaptive
integration allows to merge low-order numerical integration with rougher spatial
discretisations, reducing the number of required integration points and of
discretisation nodes.
A second section of the article investigates the efficiency of (variations on) the
Newton-Raphson scheme. It will be demonstrated that appropriate application of
Newton-Raphson on the boundary conditions, of modified iteration and of separate
convergence criteria can drastically diminish the number of required (de)
compositions.