A two step viscothermal acoustic FE method
Previously, the authors presented a finite element for viscothermal acoustics. This element has the velocity vector, the temperature and the pressure as degrees of freedom. It can be used, for example, to model sound propagation in miniature acoustical transducers. Unfortunately, the large number of coupled degrees of freedom can make the models big and time consuming to solve. A method with reduced calculation time has been developed. It is possible to partially decouple the temperature degree of freedom, as result of the differences in the characteristic length scales of acoustics and heat conduction. This leads to a method that uses two sequential steps. In the first step, a scalar field containing information about the thermal effects is calculated (not the temperature). This is a relatively small FE calculation. In the second step, the actual viscothermal acoustical equations are solved. This calculation uses the field calculated in the first step and has the velocity vector and the pressure as the degrees of freedom. The temperature is not a degree of freedom anymore, but it can be easily calculated in a post processing step. The required computational effort is reduced significantly, while the difference in the results, compared to the fully coupled method, is negligible. Along with the theoretical basis for the method, a specific FE calculation is presented to illustrate its accuracy and improvement in calculation time.
Modelling of acoustic viscothermal losses using the Boundary Element Method: From method to optimization
A range of acoustic engineering problems require the inclusion of viscous and thermal dissipation to be modelled accurately. The dissipative effects are especially relevant when the geometric dimensions of the acoustic domain become small which is the case in acoustic transducers and hearing aids. Computer-based numerical tools such as the Finite Element Method can be used to model and investigate the performance of acoustic devices without expensive prototyping. Directly including acoustic dissipation into the Finite Element Method comes at a significant computational cost, sometimes making simulations on modest hardware problematic. An interesting alternative to the Finite Element Method, is the Boundary Element Method that is capable of including dissipation and at the same time avoid so-called boundary layer meshing. However, a potential shortcoming of the existing boundary element implementation is its use of tangential derivative finite difference coupling terms, that may lead to undesirable inaccuracies. This work presents two new coupling strategies that avoid the use of finite difference by either using boundary element itself or the shape functions to estimate the tangential derivatives. Numerical experiments demonstrate increased stability and error reduction when using the new coupling strategies. Furthermore, based on the improved viscothermal Boundary Element Method, a gradient-based shape optimization technique is developed. The shape optimization technique is used to optimize the absorption coefficient of two-dimensional quartewave and Helmholtz resonators located at an impedance tube termination. Shape optimization results show that high absorption coefficients are only obtained when viscous and thermal dissipation is modelled accurately. The shape optimization technique has the future potential of improving the design of acoustic devices which require the inclusion of viscous and thermal dissipation.
Atmospheric drag effects on the KOMPSAT-1 satellite during geomagnetic superstorms
We examine the atmospheric drag on the low earth-orbiting satellite, KOMPSAT-1 in a sun-synchronous orbit at ~685-km altitude starting in 1999, during a 3-month (October-December) period in 2003. This 3-month interval includes the October 29-30 and November 20 magnetic superstorms and weak to moderate storms. We observed that the daily KOMPSAT-1 drag acceleration transiently responses to transient storm-time disturbances. That is, there is an one-to-one correspondence between the KOMPSAT-1 drag accelerations and the storm events. We find that the drag acceleration correlates strongly with the level of geomagnetic disturbance. This indicates that the trajectory of KOMPSAT-1 is significantly perturbed during extremely disturbed intervals because of atmospheric density increase. The main contributor to the density increase is Joule heating associated with the geomagnetic activity rather than the solar EUV radiation, as reported by previous studies. We suggest that understanding how the upper atmosphere responses to the geomagnetic-associated heating is important to predict space weather impacts on low earth-orbiting satellites.