What are the advantages and limitations of vortex methods for simulating inviscid flows in CFD?

2 What are the advantages of vortex methods?

Vortex methods have several advantages over other CFD methods for inviscid flows. First, they are naturally adaptive, meaning that they can concentrate the computational resources on the regions where the flow is complex and turbulent, while using fewer vortices in the regions where the flow is smooth and uniform. Second, they are free of numerical diffusion, meaning that they can preserve the circulation and the vorticity of the flow without artificial dissipation or dispersion. Third, they are compatible with unbounded domains, meaning that they do not require artificial boundary conditions at the far-field or the infinity, which can introduce errors or instabilities in other methods.

3 What are the limitations of vortex methods?

Vortex methods also have some limitations that restrict their applicability and efficiency for inviscid flows. First, they are not suitable for flows with shocks, compressibility, or heat transfer, since these phenomena involve changes in the density, temperature, and entropy of the fluid, which are not captured by the vorticity formulation. Second, they are computationally expensive, especially for three-dimensional flows, since they require a large number of vortices and a complex algorithm to compute the velocity field from the vorticity field. Third, they are sensitive to the choice of the vortex model, such as the shape, size, and distribution of the vortices, which can affect the accuracy and stability of the solution.

4 How are vortex methods implemented in CFD?

Vortex methods can be implemented in CFD using different approaches, depending on the type and geometry of the flow. One common approach is the panel method, which uses flat or curved panels to represent the solid boundaries and generates vortices along the panel edges. Another common approach is the particle method, which uses discrete particles to represent the vortices and tracks their positions and strengths using Lagrangian methods. A third approach is the grid method, which uses a fixed or moving grid to discretize the vorticity field and applies Eulerian methods to update the vorticity and velocity fields.