Abstract The secret to the spectacular flight capabilities of flapping insects lies in their wings, which are often approximated as flat, rigid plates. Real wings are however delicate structures, composed of veins and membranes, and can undergo significant deformation. In the present work, we present detailed numerical simulations of such deformable wings. Our results are obtained with a fluid–structure interaction solver, coupling a mass–spring model for the flexible wing with a pseudo-spectral code solving the incompressible Navier–Stokes equations. We impose the no-slip boundary condition through the volume penalization method; the time-dependent complex geometry is then completely described by a mask function. This allows solving the governing equations of the fluid on a regular Cartesian grid. Our implementation for massively parallel computers allows us to perform high resolution computations with up to 500 million grid points. The mass–spring model uses a functional approach, thus modeling the different mechanical behaviors of the veins and the membranes of the wing. We perform a series of numerical simulations of a flexible revolving bumblebee wing at a Reynolds number R e = 1800 . In order to assess the influence of wing flexibility on the aerodynamics, we vary the elasticity parameters and study rigid, flexible and highly flexible wing models. Code validation is carried out by computing classical benchmarks.

中文翻译：

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质量弹簧流固耦合求解器：应用于柔性旋转翼

摘要 扑翼昆虫惊人飞行能力的秘密在于它们的翅膀，它们通常被近似为扁平的刚性板。然而，真正的翅膀是由静脉和膜组成的精致结构，并且会发生显着的变形。在目前的工作中，我们提供了这种可变形机翼的详细数值模拟。我们的结果是通过流体-结构相互作用求解器获得的，将柔性翼的质量-弹簧模型与求解不可压缩 Navier-Stokes 方程的伪谱代码耦合。我们通过体积惩罚方法施加无滑移边界条件；然后，依赖于时间的复杂几何图形完全由掩码函数描述。这允许在常规笛卡尔网格上求解流体的控制方程。我们对大规模并行计算机的实现使我们能够执行高达 5 亿个网格点的高分辨率计算。质量-弹簧模型使用功能方法，从而对机翼的静脉和膜的不同机械行为进行建模。我们对雷诺数 Re = 1800 的灵活旋转大黄蜂机翼进行了一系列数值模拟。为了评估机翼柔性对空气动力学的影响，我们改变弹性参数并研究刚性、柔性和高柔性机翼模型。代码验证是通过计算经典基准来执行的。从而模拟机翼的静脉和膜的不同机械行为。我们对雷诺数 Re = 1800 的灵活旋转大黄蜂机翼进行了一系列数值模拟。为了评估机翼柔性对空气动力学的影响，我们改变弹性参数并研究刚性、柔性和高柔性机翼模型。代码验证是通过计算经典基准来执行的。从而模拟机翼的静脉和膜的不同机械行为。我们对雷诺数 Re = 1800 的灵活旋转大黄蜂机翼进行了一系列数值模拟。为了评估机翼柔性对空气动力学的影响，我们改变弹性参数并研究刚性、柔性和高柔性机翼模型。代码验证是通过计算经典基准来执行的。