Simulation and Visualization Methods for Wave Propagation in Non‐Homogeneous Media

U ovom radu razvijena je, u kodu implementirana i ispitana proširena metoda praćenja snopova (PMPS). Analizom postojećih metoda simulacija širenja zvučnih valova zapaženo je da još nije razvijena metoda širenja snopova, koja bi mogla ravnopravno tretirati refleksiju i refrakciju vala. Cilj takve, proširene, metode praćenja snopova je simulirati širenje zvuka u nehomogenim sredinama, odnosno u onim sredinama, gdje se val ne širi samo jednim medijem ili gdje se fizikalne karakteristike medija u kojem se val širi mijenjaju. Prilikom razvoja metode definirana je nova struktura scene sastavljena od entiteta, ljuski i graničnih ploha. Ovakva struktura scene omogućava definiranje nekonkveksne sredine, koja sadrži više medija. Geometrija scene temeljena je na nepravilnim trokutastim mrežama. Snopovi koji se koriste za praćenje širenja zvuka trokutastog su presjeka, a prilikom širenja se prilagođavaju okolini, odnosno vrši se podjela snopova, prigodom nailaska na diskontinuitet. Razvijen je i ispitan algoritam dijeljenja trokutastih snopova, radi prilagođavanja okolnoj geometriji. Ovaj algoritam temelji se na postupku presjeka i oduzimanja dva trokuta u ravnini, koji je u suštini drugačiji u odnosu na dosad uobičajeni Southerland‐Hodsonov algoritam. Prilikom proračuna geometrije refraktiranih snopova, ustanovljeno je i analizirano odstupanje, koje nastaje kao rezultat nelinearnosti refrakcije. Analiza je pokazala da je za uske snopove i za male razlike u brzini zvuka između dvaju medija moguće zanemariti ova odstupanja. Konačni rezultat simulacije je plošni skenom prostora, koji daje vrijednosti razine intenziteta zvuka u pojedinim točkama. Izračun razine intenziteta zvuka nov je u odnosu na tradicionalnu metodu izračuna kod simulacije širenjem snopova. Ovaj novi način izračuna donosi povećanu brzinu i fleksibilnost kod simulacije drugih valnih fenomena, a nauštrb određene greške koja se188 uvodi u proračun. Ova greška se pokazala zanemarivom i to najprije temeljem teoretske analize, a potom i prilikom mjerenja. Prilikom mjerenja na tri ispitne scene ustanovljeni su rezultati, te vremenske i prostorne performanse simulacije. Usporedbom sa dvije komercijalne simulacije prostorne akustike, temeljene na metodi praćenja zraka, potvrđeno je da PMPS daje ispravne rezultate. Vremenske i prostorne performanse simulacije bile su u razini one brže od dvije simulacije s kojima je uspoređena. Prilikom usporedbe jedina mana PMPS‐a bila je simuliranje refleksija višeg reda, koje je uzrokovalo stupanjski porast vremenskih i prostornih performansi. Najveću prednost PMPS je pokazao prilikom proračuna raspodjele zvuka velikom rezolucijom, odnosno prilikom proračuna prostora velikih dimenzija.This thesis presents the development, coding and testing of the comprehensive beam tracing method (CBTM). The present beam tracing methods for simulation of sound waves propagation do not compute the refraction, but only the reflection of sound waves. CBTM is designed for simulation of propagation of sound in non‐homogenous environments ‐ environments where the wave propagates through several media, or through one media with slightly different physical characteristics. This method has different scene structure than traditional simulations ‐ in order to enable definition of scenes with several non‐convex media, scene structure is based on boundary surfaces, shells and entities. Geometry of scene is defined using triangular irregular networks. The beams used for tracing the propagation of sound in scene have triangular section. During propagation they are adapted to surrounding geometry ‐ beam is divided when it encounters a discontinuum. This algorithm is developed specially for CBTM, and is thoroughly tested. It is based on process of intersection and subtraction of two planar triangles. The algorithm for intersection and subtraction of two planar triangles in CBTM differs from usual Southerland‐Hodgson algorithm. Construction of refracted beams in CBTM has shown slight errors in geometry of beams, which occur because refraction is a non‐linear transformation. These errors were analyzed ‐ the analysis showed that errors can be tolerated for refraction occurring between two media whose physical characteristics do not differ much, and for beams that are not wide. The final result of the simulation is the plane scan of simulated scene, which presents the level of sound intensity in raster of points in a plane. Level of sound intensity is calculated in a different fashion from traditional beam tracing simulations. This new way of calculation gives an improved performance, and possibility for extension of simulated wave phenomena, but at cost of a slight error. These errors were analyzed theoretically, and measured, with the conclusion that they can be neglected, because they are smaller than errors already incorporated in a simulation model. The CBTM was tested on three scenes, in order to check the results of simulations, and also to measure time and space performance of this method. CBTM was compared with two commercial simulations based on ray‐tracing model. The comparison showed that CBTM is accurate, and that performances of CBTM are comparable to the faster of two ray‐tracing simulations. The only drawback of CBTM that comparison discovered was that for high order of reflected sound the performance decreased exponentially. The biggest advantage of method is the very good performance in case of big resolution of plane scan, or in case of large simulated scenes