# Application of Mesh Modifications and Adjoint Error Estimates

S. Albensoeder

Abstract. Two methods for mesh modification are considered to improve hybrid meshes for CFD calculations. The first method is an adaptation with new sensors. The new sensors are based on an adjoint approach to calculate the sensitivity with respect to a goal function. Here the sensitivity of lift, drag and pitching moment was calculated with respect to the numerical dissipation terms. The second method is a local mesh modification of the unstructured part of the hybrid mesh based on an algebraic quality measure. For an a posteriori improvement the flow properties can be included to build a new anisotropic metric. Both new methods were applied to industrial relevant test cases.

1 Introduction

One problem of today computational fluid dynamics (CFD) is the discretization of the computational domain. Due to the limits of computational resources the discretization of the domain is not fine enough. Therefore the discretization can have a significant effect to the results.

A common approach to reduce this uncertainty is the adaptive refinement of the grid where errors occur. In the past several sensors (e. g. gradient based, reconstruction based) were developed to detect these underresolved regions. A sensor which computes the sensitivity of a discretization with respect to a specified goal function was introduced by [13]. The sensor was computed by solving an adjoint problem. One bottleneck of the method was that the final sensor was computed on the isotropic refined mesh instead of the original mesh. For complex configurations with a high number of grid points the demands to the computational resources are very high. In this investigation the sensors of [2] were used. This method computes the

S. Albensoeder

P3 Voith Aerospace GmbH, Flughafenallee 26, 28199 Bremen, Germany e-mail: Stefan. Albensoeder@p3voith. com

B. Eisfeld et al. (Eds.): Management & Minimisation of Uncert. & Errors, NNFM 122, pp. 55-73. DOI: 10.1007/978-3-642-36185-2_3 © Springer-Verlag Berlin Heidelberg 2013

sensitivity with respect to numerical dissipation terms. By this ansatz the error estimation can be done without any mesh refinement step.

Another approach is the improvement of a given mesh by local modifications. This improvement can be related to improve badly shaped elements and to orientate elements in the direction of the flow.

The uncertainty due to influences of the mesh generation drives the limitation that small influences can only be computed on the same or slightly modified mesh. One example is the deformation of the geometry due to aerodynamic loads. To reduce the uncertainty the whole mesh will be deformed to avoid a new meshing. Unfortunately this deformation can cause inverted elements which foreclose a new CFD computation. These cells have to be repaired which can also be done by the introduced local mesh modification.

In the next section the investigated methods are described. In section 3 the methods were applied to industrially relevant test cases. Finally a conclusion and an outlook are given.

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