Analytical and Semi-Analytical Modelling
Although numerical modeling is very powerful and versatile, it suffers from the disadvantage that fundamental relations between input and target quantities as well as their spurious cross-sensitivities are often obfuscated in the generated numerical data, and can thus only be empirically determined by time-consuming parameter studies. Therefore, sufficiently accurate analytical modeling is still preferable as it facilitates detailed insight into the impact of system-related parameters and it is generally more robust regarding device design and optimizations. Analytical modeling enables a deep insight into the system behavior at the cost of highly complex mathematical problems to be solved, which may involve complicated series or integral representations. Their evaluation is often not straightforward and must be handled with care. Consequently, both modeling and evaluation require a comprehensive knowledge in diverse mathematical fields such as (partial) differential and integral equations, higher transcendental functions, and the evaluation of series and integral equations with highly oscillating kernels. Over the years, the DISS has managed to grow a unique expertise in these fields.
Analytical modeling is often hampered due to the complexity of the problems. In order to overcome this drawback, a vast number of semi-analytical and semi-numerical methods have been established at the DISS, where analytical and numerical methods are combined in an advantageous manner. This yields representative simulation tools relevant across all research disciplines.
- For example, at the DISS, (semi-)analytical modeling is utilized to model the fully conjugated heat transfer in the flow channel as well as in the microstructure of micromachined thermal sensors. Furthermore, it is used to analyze the fluid/structure interaction of vibrating microstructures regarding excitation, coupling, and propagation of ultrasonic displacement waves in adiabatic compressible fluids with applications to novel shear and longitudinal viscosity sensor concepts. Last but not least, we exploit sophisticated (semi-)analytical models to efficiently deduce physical thin-film parameters from raw data obtained from thin-film specimen measurements.