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Most computational fluid dynamics simulations are, at present, performed in a body-fixed frame, for aeronautical purposes. With the advent of sharp manoeuvre, which may lead to transient effects originating in the acceleration of the centre of mass, there is a need to have a consistent formulation of the Navier–Stokes equations in an arbitrarily moving frame. These expressions should be in a form that allows terms to be transformed between non-inertial and inertial frames and includes gravity, viscous terms, and linear and angular acceleration. Since no effects of body acceleration appear in the inertial frame Navier–Stokes equations themselves, but only in their boundary conditions, it is useful to investigate acceleration source terms in the non-inertial frame. In this paper, a derivation of the energy equation is provided in addition to the continuity and momentum equations previously published. Relevant dimensionless constants are derived which can be used to obtain an indication of the relative significance of acceleration effects. The necessity for using computational fluid dynamics to capture nonlinear effects remains, and various implementation schemes for accelerating bodies are discussed. This theoretical treatment is intended to provide a foundation for interpretation of aerodynamic effects observed in manoeuvre, particularly for accelerating missiles. Funding agencies: DRDB [KT466921, KT528944, KT470887]

Investigation of acceleration effects on missile aerodynamics using computational fluid dynamics

The unstructured node centered finite volume method is analyzed and it is shown that it can be interpreted in the framework of summation by parts operators. It is also shown that introducing boundary conditions weakly produces strictly stable formulations. Numerical experiments corroborate the analysis.

A mathematical tool box for the analytic treatment of non-stationary problems with relatively moving frames, including an extended vector analysis in n-dimensions, has been formulated by Lofgren’ , and forms the foundation for the finite volume formulation by Forsberg’. Consider a fixed, inertial reference frame X, referred to as the absolute frame (Fig. 1). Consider also a moving reference frame Z’, which may be accelerating in an arbitrary fashion, and which is referred to as the relative frame.