Semi-exact local absorbing boundary condition for seismic wave simulation

An absorbing boundary condition is necessary in seismic wave simulation for eliminating the unwanted artificial reflections from model boundaries. Existing boundary condition methods often have a trade-off between numerical accuracy and computational efficiency. We proposed a local absorbing boundary condition for frequency-domain finite-difference modelling. The proposed method benefits from exact local plane-wave solution of the acoustic wave equation along predefined directions that effectively reduces the dispersion in other directions. This method has three features: simplicity, accuracy and efficiency. Numerical simulation demonstrated that the proposed method has higher efficiency than the conventional methods such as the second-order absorbing boundary condition and the perfectly matched layer (PML) method. Meanwhile, the proposed method shared the same low-cost feature as the first-order absorbing boundary condition method.

Effects of Tire Attributes on Aerodynamic Performance

As indicated by previous studies, many attributes of tires have been shown to have an impact on tire aerodynamic drag. However, the way these attributes affect tire aerodynamics has not been systematically investigated to date. It is not clear which tire attributes have the most significant impact on aerodynamic drag. Therefore, a sensitivity study of the effects of tire attributes on tire aerodynamic performance is proposed in this study. This sensitivity study improves the understanding of flow structures and mechanisms around tires. First, a baseline CFD model of a tire is created and validated by experimental data. In the computational model, the tire is positioned in a wind tunnel to match the experimental testing configuration. A hybrid boundary condition method is used to simulate a rotating tire. Based on the validated baseline model, various tire attributes are considered and compared in the study proposed. The tire attributes considered include tire width, tire side wall profile, lateral grooves, and open rim design. There are five cases in total for the sensitivity study. Then the effects of these attributes on the tire aerodynamic drag are calculated and compared. The most influencing feature is then identified. The results show that a smoothed side wall profile with smaller radius can improve the aerodynamic performance of an isolated tire. On the other hand, the influence of lateral grooves on tire aerodynamic performance is limited. The force integrated from all lateral groove surfaces only account to less than 2% of the total tire drag force. Additionally, an idealized open rim design changes the flow structure significantly, which leads to the increase of aerodynamic drag. The force integrated on the rim surface account for up to 20% of the overall tire drag force.

Approximate T matrix and optical properties of spheroidal particles to third order with respect to size parameter

© 2019 American Physical Society. In electromagnetic scattering, the so-called T matrix encompasses the optical response of a scatterer for any incident excitation and is most commonly defined using the basis of multipolar fields. It can therefore be viewed as a generalization of the concept of polarizability of the scatterer. We calculate here the series expansion of the T matrix for a spheroidal particle in the small-size, long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a nonspherical particle. T is calculated from the standard extended boundary condition method with a linear system involving two infinite matrices P and Q, whose matrix elements are integrals on the particle surface. We show that the limiting form of the P and Q matrices, which is different in the special case of spheroid, ensures that this Taylor expansion can be obtained by considering only multipoles of order 3 or less (i.e., dipoles, quadrupoles, and octupoles). This allows us to obtain self-contained expressions for the Taylor expansion of T(X). The lowest order is O(X3) and equivalent to the quasistatic limit or Rayleigh approximation. Expressions to order O(X5) are obtained by Taylor expansion of the integrals in P and Q followed by matrix inversion. We then apply a radiative correction scheme, which makes the resulting expressions valid up to order O(X6). Orientation-averaged extinction, scattering, and absorption cross sections are then derived. All results are compared to the exact T-matrix predictions to confirm the validity of our expressions and assess their range of applicability. For a wavelength of 400 nm, the new approximation remains valid (within 1% error) up to particle dimensions of the order of 100-200 nm depending on the exact parameters (aspect ratio and material). These results provide a relatively simple and computationally friendly alternative to the standard T-matrix method for spheroidal particles smaller than the wavelength, in a size range much larger than for the commonly used Rayleigh approximation.

Approximate T matrix and optical properties of spheroidal particles to third order with respect to size parameter

© 2019 American Physical Society. In electromagnetic scattering, the so-called T matrix encompasses the optical response of a scatterer for any incident excitation and is most commonly defined using the basis of multipolar fields. It can therefore be viewed as a generalization of the concept of polarizability of the scatterer. We calculate here the series expansion of the T matrix for a spheroidal particle in the small-size, long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a nonspherical particle. T is calculated from the standard extended boundary condition method with a linear system involving two infinite matrices P and Q, whose matrix elements are integrals on the particle surface. We show that the limiting form of the P and Q matrices, which is different in the special case of spheroid, ensures that this Taylor expansion can be obtained by considering only multipoles of order 3 or less (i.e., dipoles, quadrupoles, and octupoles). This allows us to obtain self-contained expressions for the Taylor expansion of T(X). The lowest order is O(X3) and equivalent to the quasistatic limit or Rayleigh approximation. Expressions to order O(X5) are obtained by Taylor expansion of the integrals in P and Q followed by matrix inversion. We then apply a radiative correction scheme, which makes the resulting expressions valid up to order O(X6). Orientation-averaged extinction, scattering, and absorption cross sections are then derived. All results are compared to the exact T-matrix predictions to confirm the validity of our expressions and assess their range of applicability. For a wavelength of 400 nm, the new approximation remains valid (within 1% error) up to particle dimensions of the order of 100-200 nm depending on the exact parameters (aspect ratio and material). These results provide a relatively simple and computationally friendly alternative to the standard T-matrix method for spheroidal particles smaller than the wavelength, in a size range much larger than for the commonly used Rayleigh approximation.

Approximate T matrix and optical properties of spheroidal particles to third order with respect to size parameter

© 2019 American Physical Society. In electromagnetic scattering, the so-called T matrix encompasses the optical response of a scatterer for any incident excitation and is most commonly defined using the basis of multipolar fields. It can therefore be viewed as a generalization of the concept of polarizability of the scatterer. We calculate here the series expansion of the T matrix for a spheroidal particle in the small-size, long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a nonspherical particle. T is calculated from the standard extended boundary condition method with a linear system involving two infinite matrices P and Q, whose matrix elements are integrals on the particle surface. We show that the limiting form of the P and Q matrices, which is different in the special case of spheroid, ensures that this Taylor expansion can be obtained by considering only multipoles of order 3 or less (i.e., dipoles, quadrupoles, and octupoles). This allows us to obtain self-contained expressions for the Taylor expansion of T(X). The lowest order is O(X3) and equivalent to the quasistatic limit or Rayleigh approximation. Expressions to order O(X5) are obtained by Taylor expansion of the integrals in P and Q followed by matrix inversion. We then apply a radiative correction scheme, which makes the resulting expressions valid up to order O(X6). Orientation-averaged extinction, scattering, and absorption cross sections are then derived. All results are compared to the exact T-matrix predictions to confirm the validity of our expressions and assess their range of applicability. For a wavelength of 400 nm, the new approximation remains valid (within 1% error) up to particle dimensions of the order of 100-200 nm depending on the exact parameters (aspect ratio and material). These results provide a relatively simple and computationally friendly alternative to the standard T-matrix method for spheroidal particles smaller than the wavelength, in a size range much larger than for the commonly used Rayleigh approximation.