| Vortex methods have become useful tools for the computation of incompressible fluid flow. In the present work, a vortex particle method for the simulation of unsteady two-dimensional compressible flow is developed and applied to several problems. The method is the first Lagrangian simulation method of the full compressible Navier-Stokes equations. By decomposing the velocity into irrotational and solenoidal parts, and using particles that are able to change volume and that carry vorticity, dilatation, enthalpy, entropy, and density, the equations of motion are satisfied. A general deterministic treatment of spatial derivatives in particle methods is developed by extending the method of particle strength exchange through the construction of higher-order-accurate, non-dissipative kernels for use in approximating arbitrary differential operators. The application of this technique to wave propagation problems is thoroughly explored. Remeshing of the particles and the smooth interpolation of their strengths are addressed, as is the fast summation of the velocity field. The new vortex method is applied to several model problems and their results are discussed. |
