Annual Report 2010 - Fachgruppe Informatik an der RWTH Aachen ...

computing partial derivatives for Navier--Stokes Computational Fluid Dynamics (CFD)
solvers. Such partial derivatives are needed, for instance, in sensitivity analysis and in design
optimization. Due to strong non-linearities of the solution, as well as very high memory and
runtime requirements of the simulation software, the traditional approach of approximating
the derivatives with divided differences is not appropriate in these applications, in particular
in three dimensions.
Therefore we rely on Automatic Differentiation (AD) tools for obtaining the derivatives along
with the simulation results. Using the ADIFOR tool, we augment the TFS CFD solver,
developed at the Aerodynamics Institute (AIA) of the RWTH, with code for computing
partial derivatives, in particular the derivatives of the computed velocity or pressure fields
with respect to fluid and geometrical parameters. The availability of such accurate derivative
information is crucial if the TFS code is used within some optimization framework, e.g., for
the estimation of turbulence parameters and wing shape optimization.
Furthermore, Automatic Differentiation is employed to obtain the analytic flux Jacobian for
an implicit Newton-Krylov method which is used in the recent flow solver QUADFLOW
currently under development within SFB 401. In contrast to numerical approximation of the
Jacobian, the use of AD-generated code for the Jacobian calculation generally leads to
increased performance and robustness of the overall computational method. Since in
principle, only Jacobian-vector-products are needed by the iterative method implemented in
QUADFLOW, we plan to avoid the explicit assembly of the whole Jacobian and generate
code for computing Jacobian-vector products, yielding significant savings in memory
consumption. This will also allow the transition from the currently used first-orderdiscretization
in space to a second-oder discretization scheme with improved convergence
behavior.
Towards a Computational Model of Blood Flow in the Left Human Heart, Aorta and
Connecting Vessels
M. Lülfesmann, C. Bischof, M. Bücker
The desire to understand the flow of blood through the cardiovascular system and prosthetic
devices has stimulated a flurry of activity in related fluid flow studies in recent years. This
interest stems from the need to understand the mechanism for the genesis or pathology of
cardiovascular disease and the associated cardiovascular flows. Such relationship between
blood flow and cardiovascular disease, altered physiological states, thrombus formation and
hemolysis in prosthetic devices is complex; however, a better understanding of this
relationship is essential to identify potentially pathological flow situations, recognize existing
conditions via monitoring fluid pressures and characterize the probable evolution of
pathological states. In the final analysis, one wishes to establish cause and effect protocols in
terms of primary variables and relate inaccessible variables to those that can be monitored.
This requires a detailed modeling of the cardiovascular system, encountering physiological as
well as pathological flow conditions, with and without prosthetic devices.
In this interdisciplinary JARA project, the blood flow in the natural left heart and its
proximate vascular system is modeled including the coronary arteries, the ascending aorta, the
aortic arch, and a part of the descending aorta. Collaborating partners include the following
384