The sonification of numerical fluid flow simulations

Proceedings of the 2001 International Conference on Auditory Display, Espoo, Finland, July 29-August 1, 2001When the flow is fully developed, the transverse velocity componentÚ vanishes, and the pressure Ô changes only linearly with Ü:¡Ô ½¾ÙÑ¡Ü ¾ (7)which gives the pressure drop ¡Ô over some Ü-direction length¡Ü, and where the viscosity is in this case 1 kg/ms.A coarse ¢ evenly spaced grid was used, yielding a total of ¢ ¾internal or “live” cells at which the values of Ù, Ú andÔ are updated at each iteration by the solver. With this very simpleconfiguration, the solver converges in about 20 iterations.3.1. Sonification StrategyThe purpose of this sonification was to gain insight into the solverby listening to its progress in real time. To accomplish this, 5 sineoscillators were set up to correspond to each column of “live” gridpoints. As the solver (for Ù, Ú then Ô) sweeps through the domainfrom left to right, first the column at ½sounds, from ½ ,with slight arpeggiation, and so on, with a slight pause for eachcolumn, through . Thus, each iteration produces 25 notes pervariable, for 75 total.In most CFD simulations, general trends and flow behaviorare known to the engineer in advance of the calculation. In thissonification, the pitch strategy for each variable was selected sothat the anticipated behavior in the flow direction could be “heard”:1. Development of Ù from a flat to a parabolic profile.2. Vanishing of Ú.3. Linear decrease of Ô in the flow direction.3.1.1. Pitch MappingThe values of Ù range from uniformly 1.0 at the inlet (near ½) to values in the range ¼¼ Ù ½ at the flow exit (near ). The initial guess for Ù throughout the domain is 0.0. Asthe solution iterates, values of Ù well in excess of 1.5 may result.The values of Ù were mapped to pitch and scaled so that a value ofÙ ½would yield 440 Hz, with 55 Hz set as the minimum valuefor values of Ù¼½¾.The values of Ú range from approximately 0.1 near the inletto very small numbers near the exit (the initial guess throughoutthe flow field, as for Ù, isÚ ¼¼). The values of Ú were alsomapped to pitch, but scaled up so that a value of Ú ½ wouldyield 8400 Hz. All nodes with values of Ú about ¼¼ weremapped to a major triad with pitches (150, 300, 375, 450) Hz, fornodes ¾.The values of Ô in incompressible fluid flow are generally calculatedrelative to some numerically convenient reference value,in this case Ô Ö ½¼ Pa at node ´ µ ´½ ½µ. Values of Ô arecalculated relative to Ô´½ ½µ, where the significant pressure informationis the ¡Ô between nodes which drives the flow. Using thisscheme, the values of Ô range from ¼ Ô ½¼. The localvalue of Ô was added to a different major triad (100, 200, 300, 400,500) Hz for ½. Because the values of the pressure arefairly uniform at each location, one hears, for this scheme, a successionof major triads whose pitch either increases, decreases orstays the same.3.1.2. EnvelopeThe envelope (attack, sustain, decay) characteristics were derivedfrom the matrix coefficients for each variable at each node:Ø ½ Æ ½ Æ È Ø ¾ Ë ¾ Ë È Ø ¿ (8) ¿ È Ø Ï Ï È Ø ½¼ ¼¼Equations 8 represent a 5 frame envelope where ½ is the amplitudeof the first frame, Ø ½ is its rise time, etc. The values for thefifth frame are set to constant values of 1.0 and 0.0 respectively toensure that the oscillator will turn off. The values of Ø ½ were constrainedto be at least 0.05 secs, to avoid clicks due to zero-lengthframes. Division of all neighbor coefficients Æ, etc. by the centercoefficient È ensures that ¼¼ Ò ½¼, since the centercoefficient is always greater in magnitude than its correspondingneighbors.3.1.3. DurationIn general, as the solver proceeds and makes available the latestvalues of variable and coefficient at each node, the mapped pitchesand envelopes were queued to the oscillators. However, to makethe sonic result more intelligible, some delays were added. Firstly,very slight delays were added between nodes in each column, toproduce something like an arpeggiated chord. Secondly, a longerdelay was added at the conclusion of each column, before proceedingto the next column. Thirdly, at the conclusion of the sonificationof a variable at all 25 nodes, a longer delay was added proportionalto the global error calculated for that variable. Thus, as thecalculation proceeds, this delay decreases as the error is reduced.Finally, at the conclusion of a single iteration, a longer delay wasadded. It is thus possible for the listener to distinguish, based onthe delay between notes, the different stages of the calculation.3.1.4. TimbreNo specific timbral mapping was attempted, since a sine oscillatorwas used for all notes. However, because each note was given aunique envelope, some striking timbral differences resulted, mainlyfrom different attack times.4. RESULTSThe parameter/variable mapping choices described in the previoussection had the following effects:¯ The Ù velocity sonification captured the oscillations of thesolver well. The solver initial guess of Ù ¼was followed,at the second iteration, by values considerably overshootingthe final result. This behavior sounded like a sequenceICAD01-48