Boundary Element Methods

Updated April 23, 2026

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General

The table below provides an overview of the main characteristics of each panel type used in the Boundary Element Methods (BEM) implemented in flow5.

The pros, cons and comments below reflect the author's experience with xflr5 and flow5. They should not be understood as being general conclusions applicable to all case studies or to other 3rd party programs.

The recommendation is to use the same method across all designs to ensure that results are consistent and comparable.

Description

Method Order Surface type Panel singularities B.C. Pros Cons Comment
LLT N/A Thin Continuous horseshoe vortices Neumann

Fast.

Viscous non-linear behaviour extrapolated from 2d data.

Only handles the main wing.

Does not handle volumes, e.g. fuselages.

 Implements the method described in NACA TN-1269 "METHOD FOR CALCULATING WING CHARACTERISTICS BY LIFTING-LINE THEORY USING NONLINEAR SECTION LIFT DATA".
Historically the first wing analysis method implemented in xflr5.
VLM1 Uniform Thin Horseshoe vortices Neumann

Fast.

Comparable to AVL.

Does not handle volumes, e.g. fuselages.

Does not handle sideslip in the flow5 implementation

Each horseshoe vortex sheds two trailing vortices which

  • increases signifcantly the time to calculate the induced forces
  • increases the risk of numerical interference between vortices
  • tends to smooth out the influence of local changes in the geometry

 Historically, the horseshoe vortex method is the first one developed for BEM.
VLM2 Uniform Thin Ring vortices Neumann Fast. Does not handle volumes, e.g. fuselages Mathematically close to the Quad-thin method, except for
  • The location of the control points positioned at the 3/4 chordwise length of the panel
  • The calculation of forces, pressures and moments all calculated from the Kutta-Joukowski theorem
Quads Uniform Thin Uniform source and doublets Neumann on the wings,
Dirichlet on the fuselage. 		Fast.

Mathematical formulation is exact for planar elements only. In the general case, planar quads cannot cover 3d surfaces and are warped which makes the formulation approximate.

Can handle volumes, e.g. fuselages. However in the flow5 implementation, There is no option to make the fuselage's mesh conformant to the wings' meshes. Triangle methods should be used instead.

Based on the method described in NASA-TN-4023 "Program VSAero theory document".

Mathematically close to the VLM2 method, except for

  • The location of the control points positioned at the panel's centroid
  • The calculation of forces, pressures and moments based on the gradient of local velocities

It is often mentioned in literature that the position of the control point is optimal at the panel's 3/4 chordwise point. Experiments with flow5 however do not confirm this conclusion, as the Quad-thin results seem no more or no less accurate than those of the VLM2.

Thick Uniform source and doublets Dirichlet

Thick surface methods give consistently higher induced drag and lift compared to the thin surface method.

No apparent advantage over the thin surface method.

Triangles Uniform Thin Uniform source and doublets Neumann on the wings,
Dirichlet on the fuselage.

Versatile.

Numerically robust.

Fast.

Triangles by nature can cover any 3d surface.

The fuselage mesh can be made conformant to the wings meshes.

 Requires twice the number of quad elements. The recommended method.
Thick Uniform source and doublets Dirichlet

Thick surface methods give consistently higher induced drag and lift compared to the thin surface method.

No apparent advantage over the thin surface method.

Linear Thin Linear source and doublets Neumann on the wings,
Dirichlet on the fuselage. 		The inviscid part of the solution may be slightly more accurate than in the case of the tri-uniform method.

Long computation times.

Numerically sensitive to triangle geometries.

Requires ×9 the amount of live memory compared to the tri-uniform case.

Benefit in accuracy disappears with growing mesh sizes as both the uniform and linear methods become accurate within numerical errors.

 Not recommended for lack of benefit over the tri-uniform case.
Thick Linear source and doublets Dirichlet



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