In this work we propose, analyse, and demonstrate a new adjoint-based multilevel multifidelity Monte Carlo framework called FastUQ. The framework unifies the multifidelity analysis of Ng 1 , multilevel multifidelity analysis of Geraci 2 and an adjoint error correction surrogate model due to Ghate 3. The optimal mean squared error estimator shows that introducing multilevel in a multifidelity framework guarantees reduction in computational cost. Moreover, unlike the surrogate model of Ghate 3 , the method does not suffer from the curse of dimensionality. FastUQ is demonstrated here to quantify uncertainties in aerodynamic parameters due to surface variations caused by the manufacturing processes for a highly loaded turbine cascade. A stochastic model for surface variations on the cascade is proposed and optimal dimensionality reduction of model parameters is realised using goal-based principal component analysis considering the adjoint sensitivities of multiple quantities of interest (QoI). The proposed method achieves a reduction of 70% in computational cost in predicting the mean quantities like total-pressure loss and mass flow rate compared to state-of-art MLMC method. The robustness of the method is shown in application to the highly non-linear case of a heavily loaded turbine cascade operating at off-design conditions.
We present an open-source topology-aware hierarchical unstructured mesh partitioning and load-balancing tool TreePart. The framework provides powerful abstractions to automatically detect and build hierarchical MPI topology resembling the hardware at runtime. Using this information it intelligently chooses between shared and distributed parallel algorithms for partitioning and loadbalancing. It provides a range of partitioning methods by interfacing with existing shared and distributed memory parallel partitioning libraries. It provides powerful and scalable abstractions like onesided distributed dictionaries and MPI3 shared memory based halo communicators for optimising HPC codes. The tool was successfully integrated into our in-house code and we present results from a large-eddy simulation of a combustion problem. CCS CONCEPTS • Computing methodologies → Massively parallel and highperformance simulations; Massively parallel algorithms.
Numerical shape optimisation is becoming an essential tool in aeronautic design. Highfidelity optimisation with many design variables will require gradient-based optimisation, adjoint methods can compute gradients very efficiently. CAD models are used on every stage of engineering product development from design to manufacturing. Ideally, the CAD system is kept inside the optimisation loop to maintain a consistent CAD model during the optimisation, as often practised in gradient-free optimisation. However, typical commercial CAD systems do not offer derivative computation, and standard CAD parametrisations may not define a suitable design space for the optimisation. In this work, we use the automatically differentiated (AD) version of Open Cascade Technology (OCCT) CAD-kernel, which robustly provides accurate derivatives with respect to CAD parameters. The kernel is used to handle implicit CAD parametrisations, e.g. move control points of NURBS surfaces, automatically re-parametrise these surfaces, compute intersections between them and perform corresponding mesh morphing. We apply the differentiated CAD tool and parametrisation to high-fidelity aerodynamic shape optimisation of the NASA CRM wing-body intersection and exercise the CAD method for the pylon-nacelle modification.
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