For my masters thesis, I want to work in aerodynamics but quite confused in panel methods like Discrete vortex method and CFD. I read somewhere that CFD has replaced panel methods to a large extent.
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In general, CFD solvers are based on the Navier-Stokes equations, which considers the viscosity of the fluid1. The effect of fluid viscosity generates vorticity (rotation motion). Due to the nature of the Navier-Stokes equations, the most efficient way to solve it (for a given problem) is to discretize the equations and use a numerical method to solve the resulting system of equations (usually the finite volume method, or finite elements).
When the viscosity of the fluid is neglected (inviscid "fluid"), the flow tends to be irrotational (null vorticity), and due to a vector identity (∇x∇scalar function = 0), the flow velocity field, v, can be described as the gradient of a scalar function, called velocity potential, : v =∇Φ. The flow given by v is called the potential flow. Calculating the divergence of v, a Poisson equation is obtained for the velocity potential (∇²Φ = f(x,y,z) ). To solve the Poisson equation we have two options:
1 - use the finite element method, which requires dicretization of the fluid domain (numerical mesh),
2 - use the fundamental solution, determined via an integral equation (Green's second identity), which basically requires only the discretization of the body.
Notoriously, the second option is simpler to implement and requires less computational effort.
In external flow problems (aerodynamics), the fluid domain is the entire region around the boundary of the body, and extends to infinity. If the flow is potential, it is possible to calculate the velocity potential anywhere in the fluid domain (and therefore, by derivation the velocity field), as long as the potential and its normal derivative are known at the domain boundaries (basically the body boundary ). For flow around complex geometries, the integral equation is discretized into elements that were called panels (panel method). Therefore, the panel method is a numerical method that uses integral equations to solve the kinematics of the invicid (irrotational) flow around bodies. The dynamics of inviscd flow is treated with the Bernoulli equation (degeneration of the Navier-Stokes equation for the incompressible and irrotational flow case).
I have never worked with the discrete vortex method, but in general, this method uses the Lagrangean approach to describe the viscous flow motion around bodies.
"I read somewhere that CFD has replaced panel methods to a large extent."
This is true, but you should be aware of the following aspects.
- In the 60s, 70s, computational performance was poor, so using the potential approach was an advantage, as the calculation was fast. For this purpose, the so-called viscous/inviscid interaction methods were developed, widely used in aircraft and vessel designs (cases in which the flow has a high Reynolds number ). With the fast increase in computational performance, the potential approach was losing ''steam''. Thus, the models for calculating the of viscous fluids motion (including turbulence) could be solved with an increasingly lower computational cost.
- However, if you, or your institution, do not have a high-performance computer, the cost to calculate the viscous flow using CFD can still be very high - unsteady, three-dimensional flow -. That is why the viscous/inviscid interaction methods are still being developed, which use the potential approach (low computational cost) to somehow make the calculation of the viscous flow more efficient. In addition, there is the side of scientific research in the viscous/inviscid interaction that is still under development, while in the CFD, in general, the individual acts more as a user (unless you develop your code).
1 Although CFD is linked to viscous flow resolution, CFD is any numerical method that solves the fluids motion.
Yes you read correctly, CFD has replaced panel methods to a large extent and it is more relevant in Aerodynamics but Panel Method is also equally important if you are not interested in viscous effect.
Panel methods are best for model design analysis owing to their fast turnaround time and comparatively straightforward, but this is contradicted by the panel method's incompetence to calculate boundary layers and recirculation length.
In some cases, the viscous effects are not significant and the panel methods are ideal for such cases.
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