Principle of the ring-guided procedure. Case . For one source time [(a) and (b)] and the following [(c) and (d)], at high emission angle [(a) and (c)] a low emission angle [(b) and (d)]. The procedure tracks observer grid points located between the two full-line circles (bold crosses) while minimizing the number of useless tested points (squares). The dotted-line circles correspond to other source times, and are plotted for visual aid.
CPU-time of test simulations with respect to the number of source-observer pairs, for different grid combination. (a) scanning emission-time procedure; (b) ring-guided emission-time procedure [solid line from estimation (9)].
Snapshots of the fluctuating pressure, density, dilatation, vorticity and Lighthill’s source term (from top to bottom). The high speed flow is on top.
Respective amplitudes (black boxes) and acoustic powers (gray boxes) of the subterms of Eq. (10), in the source domain. The value corresponds to the full Lighthill source term.
Fluctuating pressure fields for a mixing layer. (a) direct computation (reference solution); (b) result from Lighthill’s analogy.
Radial profile of acoustic pressure obtained from the acoustic analogy (symbols), source position , solid and dashed lines represent and decay respectively.
Fluctuating pressure fields resulting from (a) summed contributions of driving source subterms , (b) summed contributions of subterms and 7, (c) summed contributions of subterms and subterms 5 and 7. (d) the subterm 1 alone; (e) summed contributions of subterms , (f) summed contributions of subterms .
Single source point test case. (a) Account of observer points concerned by the procedure marching as a function of the ring radius . (b) Dependency on of proportionality ratios between the number of points located on the ring, or outside it, and the ring radius .
(a) CPU-time and accounts of observer points concerned by the procedure marching as a function of the ring radius, for real source and observer domains, with different source grids. (b) CPU-time by ring step as a function of the number of [source-observer] pairs of which distance is between and . Each symbol corresponds to a source file time step, that is an entire value of .
Evolution of coefficient with . Symbols: different observer grids for ; straight line: linear regression.
Algorithm 1. Sketch of a reception time algorithm (instructions 1 and 9 are optional).
Algorithm 2. Sketch of an emission time algorithm.
Algorithm 3. Sketch of a ring-guided emission time algorithm (instructions 4 and 7 are optional).
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