Methodologies
Hybrid CFD/Panel Method
Computational fluid dynamics (CFD) based on finite volume method (FVM) is the most famous simulation method in fluid mechanics. It is a Eulerian approach to predict flow fields near objects. However, it requires high computational cost even with state of the art computing environment using parallel computation.
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Panel method is an useful method that computes surface flows (not field) based on the potential flow. It is very fast and moderately accurate in high Reynolds flow that the vicous flow can be neglected, thus it was a main solver in the industy during the past dacades. But, the accuracy is not sufficient when the flow is nonlinear as the method is based on linear Laplace's equation.
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A hybrid CFD/panel method is an efficient method to couple both of the CFD and the panel method. It can compute nonlinear flows near the objects and linear flows at far from them. Using this method, accurate flow simulation results can be obtained quickly.
Non-Linear Vortex Lattice Method
A conventional vortex lattice method (VLM) is a Lagrangian approach based on the Laplace's equation. It is more simplified version of the panel method assuming the thin airfoil theory. VLM is more faster than the panel method. But, it is still inaccurate in nonlinear flow simulations.
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A nonlinear LVM (NVLM) is a modified version of the conventional VLM. The nonlienar flow effects are added to the linear flow solution computed by VLM. It is done by using a table look-up method. A table is constructed with experiments or the CFD for 2-D sectional shapes of 3-D objects, which have nonlinear flow effects. This is an indirect method to simulate nonlinear flows but it is fast compared to CFD, and the simulation accuracy is comparable with CFD.
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UAV and PAV rotors generate low Reynolds number flows that the nonlinear viscous flow occurs. It thos cases, VLM is not accurate and NVLM is needed.
Fast Multi-Pole Method (FMM)
A conventional vortex lattice method (VLM) is a Lagrangian approach based on the Laplace's equation. It is more simplified version of the panel method assuming the thin airfoil theory. VLM is more faster than the panel method. But, it is still inaccurate in nonlinear flow simulations.
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A nonlinear LVM (NVLM) is a modified version of the conventional VLM. The nonlienar flow effects are added to the linear flow solution computed by VLM. It is done by using a table look-up method. A table is constructed with experiments or the CFD for 2-D sectional shapes of 3-D objects, which have nonlinear flow effects. This is an indirect method to simulate nonlinear flows but it is fast compared to CFD, and the simulation accuracy is comparable with CFD.
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UAV and PAV rotors generate low Reynolds number flows that the nonlinear viscous flow occurs. It thos cases, VLM is not accurate and NVLM is needed.
Vortex-In-Cell (VIC) Method
A conventional vortex lattice method (VLM) is a Lagrangian approach based on the Laplace's equation. It is more simplified version of the panel method assuming the thin airfoil theory. VLM is more faster than the panel method. But, it is still inaccurate in nonlinear flow simulations.
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A nonlinear LVM (NVLM) is a modified version of the conventional VLM. The nonlienar flow effects are added to the linear flow solution computed by VLM. It is done by using a table look-up method. A table is constructed with experiments or the CFD for 2-D sectional shapes of 3-D objects, which have nonlinear flow effects. This is an indirect method to simulate nonlinear flows but it is fast compared to CFD, and the simulation accuracy is comparable with CFD.
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UAV and PAV rotors generate low Reynolds number flows that the nonlinear viscous flow occurs. It thos cases, VLM is not accurate and NVLM is needed.
Variable-Fidelity(VF) Kriging Method
Global optimization methods such as a genetic algorithm and a particle swarm need to evaluate an objective function for a design candidate, and there are lots of candidates during the optimization process. In aerospace engineering, the function evaluation for each candidate is typically done by computer simulations which the cost is very expensive.
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A response surface (RS) model is to model a design space for the objective function mathematically in order to search the design space very quickly. there are widely used RS models such as Radial Basis Funtion (RBF), Support Vector Regression (SVR), and Kriging. Among them, the Kriging model is the most famous in Aerospace engineering because it can model highly non-linear design spaces well.
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Variable-fidelity (of multi-fidelity) simulation is simultaneous usage of multiple number of simulation methods with different model fidelity. It can be various combination of methods such as the vortex lattice method (VLM) for low-fidelity and finite-volume method (FVM) for high-fidelity. Or even experimental data can be for the high-fidelity assuming that the data is obtained accurately. The purpose is to obtain a high-fidelity simulation result at low computational cost. For the response surface model, the low-fidelity data is used to model the overall trend of a design space, whereas the high-fidelity data is used to correct the local accuracy of the design space.
Dynamic Fidelity Indicator for VF Kriging
When the VF response surface model is used to model a design space, the fidelity needs to be determined for each design point. Dynamic fidelity indicator (DFI) is a statistical decision making model for that. The fundamental is to select appropriate fidelity of simulation statistically using Bayesian inference. It is based on the Kriging model, thus DFI is updated during a design process.
