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Extra resources for A COMPILL4TIBN OF THE MATHEMATICS LEADING TO THE DOUBLET LKI TICE METHOD
In other words, six simultaneous pulses are transmitted to the point (x,, yo, z,) with a different delay. Now, instead of pulsing simultaneously, we pulse the sources in a sequence, starting with the sonrce at 4, and ending with the source at 46' Each source is pulsed with a time delay of t = r, relative to t = 0. Furthermore, rather than a unit strength, each source is pulsed with strength F1 . Equation (123) now takes the form 6 4(X"',Y",Z" 0, 1 F)8 t-T (124) Instead of six point sources, we may have many point sources along the xoaxis.
The Far Field Boundary Condition The far field boundary condition is enforced at far distances from the interior boundary where the flow is uniform. It will be clear that the far field condition is satisfied automatically when one uses a superposition of sources or doublets on the interior boundary. The influence of sources and doublets dies out at infinite distances. 31 Linearized Boundaxy Conditions from Firt Principles The nrailing Wake Boundary Condition Steady state lift cannot be sustained where there is no viscosity.
We could have a non-planar wake. ) It is assummed that there is no jump in the non-zero velocity component, w = •z across the wake. Therefore, 4, is symmetric with respect to z in its first approximation (eg. Fourier Series) with respect to z . With 4, symmetric, it follows that ý, •x and 0, are all antisymmetric with respect to z in the first approximation. Therefore the pressure 1. See Sections 13-8 through 13-10 of Karaincheti for a discussion of the wake. CMapter 7 discusses flow discontinuity 2.
A COMPILL4TIBN OF THE MATHEMATICS LEADING TO THE DOUBLET LKI TICE METHOD