Comparative Study Of Different Schemes Research Articles

A Comparative Study of Different Schemes Based on Bézier-like Functions with an Application of Craniofacial Fractures Reconstruction

Cranial implants, especially custom made implants, are complex, important and necessary in craniofacial fracture restoration surgery. However, the classical procedure of the manual design of the implant is time consuming and complicated. Different computer-based techniques proposed by different researchers, including CAD/CAM, mirroring, reference skull, thin plate spline and radial basis functions have been used for cranial implant restoration. Computer Aided Geometric Design (CAGD) has also been used in bio-modeling and specifically for the restoration of cranial defects in form of different spline curves, namely C1,C2,GC1GC2, rational curves, B-spline and Non-Uniform Rational B-Spline (NURBS) curves. This paper gives an in-depth comparison of existing techniques by highlighting the limitations and advantage in different contexts. The construction of craniofacial fractures is made using different Bézier-like functions (Ball, Bernstein and Timmer basis functions) and is analyzed in detail. The C1,GC1 and GC2 cubic Ball curves are performed well for construction of the small fractured part. Any form of fracture is constructed using this approach and it has been effectively applied to frontal and parietal bone fractures. However, B-spline and NURBS curves can be used for any type of fractured parts and are more friendly user.

Analysis of numerical methods to solve one-dimensional fluid-dynamic governing equations under impulsive flow in tapered ducts

A comparative study of different schemes to solve one-dimensional (1-D) gas flow equations in tapered pipes was conducted in this paper. The total variation diminishing schemes, flux corrected transport techniques or the innovative space–time conservation element and solution element method have been contrasted with experimental data. The experimental results were obtained with an impulsive flow test rig, where isolated pressure pulses can be generated in order to study the flow-dynamic behaviour of different components, including tapered pipes. The results of the different schemes were compared to the experimental data and a fairly good agreement was achieved when high-resolution schemes were used but with a considerable increment of computational effort. A mass conservation study through the tapered ducts with impulsive flow was also carried out, which demonstrated that it is not the resolution level of the scheme but the governing equations arrangement that has decisive importance in mass conservation.