A Vortex Particle Method for Two-Dimensional Compressible Flow

Abstract

A vortex particle method is developed for simulating two-dimensional, unsteady compressible flow. The method uses the Helmholtz decomposition of the velocity field to separately treat the irrotational and solenoidal portions of the flow, and the particles are allowed to change volume to conserve mass. In addition to having vorticity and dilatation properties, the particles also carry density, enthalpy, and entropy. The resulting evolution equations contain terms that are computed with techniques used in some incompressible methods. Truncation of unbounded domains via a nonreflecting boundary condition is also considered. The fast multipole method is adapted to compressible particles in order to make the method computationally efficient. The new method is applied to several problems, including sound generation by corotating vortices and generation of vorticity by baroclinic torque. c 2002 Elsevier Science (USA)

A General Deterministic Treatment of Derivatives in Particle Methods

“…For computing derivatives near the edge of the computational domain, we developed one-sided integral operators which only look inward for information. Such a treatment is used for enforcing a nonreflecting boundary condition by Eldredge et al [9] and could be applied to wall-bounded flows as an alternative to the image treatment employed by Ploumhans and Winckelmans [15]. The dispersive character of PSE was explored and it was found that only high-order-accurate kernels should be used in these contexts.…”

“…These new kernels allow many new applications of PSE, particularly in wave propagation problems, but also in the baroclinic term in vortex particle methods for compressible flows [9] and other contexts not listed.…”

“…In SPH the gradient of the pressure is computed. The compressible VPM of Eldredge et al [9] requires calculation of the Laplacian of the enthalpy, as well as gradients of enthalpy and entropy in the baroclinic term. The challenge in each of these methods lies in accurately computing the derivative of a quantity from information only available at scattered locations.…”

“…The vortex particle method (VPM) has become a useful tool for computing incompressible flows in which vorticity is an integral component [5], and recently, the VPM has been adapted to compressible flows by Eldredge et al [9]. The method of smoothed particle hydrodynamics (SPH) is applied in the contexts of astrophysical fluid dynamics and gas dynamics [11].…”

Calculation of the Acoustic Spectrum of a Cylindrical Vortex in Viscous Heat-Conducting Gas Based on the Navier–Stokes Equations

“…Research on the radiation of vortex systems has been conducted in [3] (system of two vortex rings) and [4] (system of four cylindrical vortices). The computations were performed with the aid of a vortex particle method [5]. Analysis of perturbation energy of eddy flows in connection with the problem of stability was considered in [6][7][8][9].…”