The purpose of our work is to develop an automatic shape optimization tool for runner wheel blades in reaction water turbines, especially in Kaplan turbines. The fluid flow is simulated using an in-house incompressible turbulent flow solver based on recently introduced isogeometric analysis (see e.g. J. A. Cotrell et al.: Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, 2009). The proposed automatic shape optimization approach is based on a so-called hybrid optimization which combines...
We derive a posteriori error estimates for singularly
perturbed reaction–diffusion problems which yield a guaranteed
upper bound on the discretization error and are fully and easily
computable. Moreover, they are also locally efficient and robust in
the sense that they represent local lower bounds for the actual
error, up to a generic constant independent in particular of the
reaction coefficient. We present our results in the framework of
the vertex-centered finite volume method but their nature...
In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup
stability constants is essential. In [Huynh et al., C. R. Acad.
Sci. Paris Ser. I Math.345 (2007) 473–478], the authors presented an efficient
method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to
minimizing a linear functional under a few linear constraints. These constraints...