A.3 Numerical Results As detailed in Section A.2, RBIE has a different formulation which yields different dispersion errors. In Figure A.2, the dispersion error for the RBIE with the second order polynomial approximation (RBIE-m=6) is shown for the propagation angle . It can be observed that an increase of the radius of influence domain leads to more accurate results in the range . For the error still remains less than 10-2 which kh=2, indicates lower dispersion in comparison to LBIE for this particular case (See Figure 4.12b). In the range , is preferable to the other two cases. rinfl=4h Figure A.2: Dispersion error vs. the non-dimensionalized exact wavenumber for the propagation angle . In Figure A.3, the results obtained for RBIE-m=6, RBIEand RBIE-RBF- for are kh=1, shown. Recalling Figure 4.12a, RBIE perform at the same order of accuracy with the LBIE methods, when or however RBIE produces less accurate rinfl=3h rinfl=4h, results by one order of magnitude when RBIE-is the most accurate of the rinfl=2h. RBIE methods in general with the exceptions obviously occurring when the propagation angle is very different from. Figure A.3: Dispersion over the propagation angle for the non-dimensional wavenumber; (a) (b) and (c) rinfl=2h, rinfl=3h rinfl=4h.
A.3 Numerical Results As detailed in Section A.2, RBIE has a different formulation which yields different dispersion errors. In Figure A.2, the dispersion error for the RBIE with the second order polynomial approximation (RBIE-m=6) is shown for the propagation angle . It can be observed that an increase of the radius of influence domain leads to more accurate results in the range . For kh=2, the error still remains less than 10-2 which indicates lower dispersion in comparison to LBIE for this particular case (See Figure 4.12b). In the range , rinfl=4h is preferable to the other two cases. Figure A.2: Dispersion error vs. the non-dimensionalized exact wavenumber for the propagation angle . In Figure A.3, the results obtained for RBIE-m=6, RBIEand RBIE-RBF- for kh=1, are shown. Recalling Figure 4.12a, RBIE perform at the same order of accuracy with the LBIE methods, when rinfl=3h or rinfl=4h, however RBIE produces less accurate results by one order of magnitude when rinfl=2h. RBIE-is the most accurate of the RBIE methods in general with the exceptions obviously occurring when the propagation angle is very different from. Figure A.3: Dispersion over the propagation angle for the non-dimensional wavenumber; (a) rinfl=2h, (b) rinfl=3h and (c) rinfl=4h.
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