and are the discrete indices referring to the difference of the locations of the γ1 γ2 two field points considered (in and directions, respectively). In the LBIE-RBF, x y given a constant size of influence domain, a discrete form of the equation (3.30) is written for the interior nodes as; (3.49) with being the normalized (with distances of the furthest neighbouring nodal s1,s2 h) points which remain within the influence domain of (q1,q2) in and directions, x y respectively. Here, is the coefficient of the potential value arising in the discretized form of the equation (3.30) written for the node at (q1,q2). By assuming the harmonic evolution of the acoustic pressure of the nodal values given by (3.48), equation (3.49) becomes; (3.50) For a non-zero distribution of the acoustic pressure, it is evident from equation uh, (3.50) that the numerical wavenumber can be determined, for given values of and k the angle of propagation, by solving; (3.51) Throughout this thesis the results for dispersion are presented as Dispersion error: follows; (3.52)
γ1 and γ2 are the discrete indices referring to the difference of the locations of the two field points considered (in x and y directions, respectively). In the LBIE-RBF, given a constant size of influence domain, a discrete form of the equation (3.30) is written for the interior nodes as; (3.49) with s1,s2 being the normalized (with h) distances of the furthest neighbouring nodal points which remain within the influence domain of (q1,q2) in x and y directions, respectively. Here, is the coefficient of the potential value arising in the discretized form of the equation (3.30) written for the node at (q1,q2). By assuming the harmonic evolution of the acoustic pressure of the nodal values given by (3.48), equation (3.49) becomes; (3.50) For a non-zero distribution of the acoustic pressure, uh, it is evident from equation (3.50) that the numerical wavenumber can be determined, for given values of k and the angle of propagation, by solving; (3.51) Dispersion error: Throughout this thesis the results for dispersion are presented as follows; (3.52)
Thesis_Hakan_Dogan.docx