This chapter discusses pressure calculations and aerodynamic forces in external flows. The dynamic variables are recovered from the kinematic velocity-vorticity formulation of the Navier-Stokes equations. Both velocity and vorticity fields may result from vortex methods. In the example presented, the kinematic variables are generated from the stochastic vortex blob simulation of the viscous incompressible flow. The vorticity field is a discontinuous function. This contribution demonstrates how to find pressure as a solution to the variational problem which forms a weak version of the momentum equation. It does not require any explicit boundary conditions for pressure, and no derivatives of vorticity have to be calculated in this approach. The correctness of the calculation of the pressure field and consequently of the aerodynamic forces is verified by an alternative method of calculating the aerodynamic forces which directly applies formulas involving the velocity and vorticity fields.

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Calculation of Pressure and Forces in Stochastic Vortex Methods

  • Andrzej F. Nowakowski

摘要

This chapter discusses pressure calculations and aerodynamic forces in external flows. The dynamic variables are recovered from the kinematic velocity-vorticity formulation of the Navier-Stokes equations. Both velocity and vorticity fields may result from vortex methods. In the example presented, the kinematic variables are generated from the stochastic vortex blob simulation of the viscous incompressible flow. The vorticity field is a discontinuous function. This contribution demonstrates how to find pressure as a solution to the variational problem which forms a weak version of the momentum equation. It does not require any explicit boundary conditions for pressure, and no derivatives of vorticity have to be calculated in this approach. The correctness of the calculation of the pressure field and consequently of the aerodynamic forces is verified by an alternative method of calculating the aerodynamic forces which directly applies formulas involving the velocity and vorticity fields.