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This paper aims to apply the novel numerical model to analyze the effect of pillar material on the response of compound quartz crystal resonator (QCR) with an array of pillars. The performance of the proposed device compared to conventional QCR method was also investigated.

A finite element method model was developed to analyze the behavior of QCR coupled with an array of pillars. The model was composed of an elastic pillar, a solution and a perfectly matched layer. The validation of the model was performed through a comparison between its predictions and previous experimental measurements. Notably, a good agreement was observed between the predicted results and the experimental data.

The effect of pillar Young’s modulus on the coupled QCR and pillars with a diameter of 20 µm, a center-to-center spacing of 40 µm and a density of 2,500 kg/m³ was investigated. The results indicate that multiple vibration modes can be obtained based on Young’s modulus. Notably, in the case of the QCR–pillar in air, the second vibration mode occurred at a critical Young’s modulus of 0.2 MPa, whereas the first mode was observed at 3.75 Mpa. The vibration phase analysis revealed phase-veering behavior at the critical Young’s modulus, which resulted in a sudden jump-and-drop frequency shift. In addition, the results show that the critical Young’s modulus is dependent on the surrounding environment of the pillar. For instance, the critical Young’s modulus for the first mode of the pillar is approximately 3.75 Mpa in air, whereas it increases to 6.5 Mpa in water.

It was concluded that the performance of coupled QCR–pillar devices significantly depends on the pillar material. Therefore, choosing pillar material at critical Young’s modulus can lead to the maximum frequency shift of coupled QCR–pillar devices. The model developed in this work helps the researchers design pillars to achieve maximum frequency shift in their measurements using coupled QCR–pillar.

The purpose of this study is to propose a precise and standardized strategy for numerically simulating vehicle aerodynamics.

Error sources in computational fluid dynamics were analyzed. Additionally, controllable experiential and discretization errors, which significantly influence the calculated results, are expounded upon. Considering the airflow mechanism around a vehicle, the computational efficiency and accuracy of each solution strategy were compared and analyzed through numerous computational cases. Finally, the most suitable numerical strategy, including the turbulence model, simplified vehicle model, calculation domain, boundary conditions, grids and discretization scheme, was identified. Two simplified vehicle models were introduced, and relevant wind tunnel tests were performed to validate the selected strategy.

Errors in vehicle computational aerodynamics mainly stem from the unreasonable simplification of the vehicle model, calculation domain, definite solution conditions, grid strategy and discretization schemes. Using the proposed standardized numerical strategy, the simulated steady and transient aerodynamic characteristics agreed well with the experimental results.

Building upon the modified Low-Reynolds Number k-e model and Scale Adaptive Simulation model, to the best of the authors’ knowledge, a precise and standardized numerical simulation strategy for vehicle aerodynamics is proposed for the first time, which can be integrated into vehicle research and design.