Adaptive numerical modeling using the hierarchical Fup basis functions and control volume isogeometric analysis

2020 ◽  
Vol 92 (10) ◽  
pp. 1437-1461 ◽  
Author(s):  
Grgo Kamber ◽  
Hrvoje Gotovac ◽  
Vedrana Kozulić ◽  
Luka Malenica ◽  
Blaž Gotovac
2021 ◽  
Author(s):  
◽  
Grgo Kamber ◽  

The main objective of this thesis is to utilize the powerful approximation properties of Fup basis functions for numerical solutions of engineering problems with highly localized steep gradients while controlling spurious numerical oscillations and describing different spatial scales. The concept of isogeometric analysis (IGA) is presented as a unified framework for multiscale representation of the geometry and solution. This fundamentally high-order approach enables the description of all fields as continuous and smooth functions by using a linear combination of spline basis functions. Classical IGA usually employs Galerkin or collocation approach using B-splines or NURBS as basis functions. However, in this thesis, a third concept in the form of control volume isogeometric analysis (CV-IGA) is used with Fup basis functions which represent infinitely smooth splines. Novel hierarchical Fup (HF) basis functions is constructed, enabling a local hp-refinement such that they can replace certain basis functions at one resolution level with new basis functions at the next resolution level that have a smaller length of the compact support (h-refinement), but also higher order (p-refinement). This hp-refinement property enables spectral convergence which is significant improvement in comparison to the hierarchical truncated B-splines which enable h-refinement and polynomial convergence. Thus, in domain zones with larger gradients, the algorithm uses smaller local spatial scales, while in other region, larger spatial scales are used, controlling the numerical error by the prescribed accuracy. The efficiency and accuracy of the adaptive algorithm is verified with some classic 1D and 2D benchmark test cases with application to the engineering problems with highly localized steep gradients and advection-dominated problems.


2017 ◽  
Vol 21 (3) ◽  
pp. 835-866 ◽  
Author(s):  
Meng Wu ◽  
Bernard Mourrain ◽  
André Galligo ◽  
Boniface Nkonga

AbstractMotivated by the magneto hydrodynamic (MHD) simulation for Tokamaks with Isogeometric analysis, we present splines defined over a rectangular mesh with a complex topological structure, i.e., with extraordinary vertices. These splines are piecewise polynomial functions of bi-degree (d,d) and parameter continuity. And we compute their dimension and exhibit basis functions called Hermite bases for bicubic spline spaces. We investigate their potential applications for solving partial differential equations (PDEs) over a physical domain in the framework of Isogeometric analysis. For instance, we analyze the property of approximation of these spline spaces for the L2-norm; we show that the optimal approximation order and numerical convergence rates are reached by setting a proper parameterization, although the fact that the basis functions are singular at extraordinary vertices.


2020 ◽  
Vol 3 (1) ◽  
pp. 10
Author(s):  
Samuel Sami

In this study, a mathematical and numerical modeling of the photovoltaic (PV)-thermal solar system to power the multistage flashing chamber process is presented. The proposed model was established after the mass and energy conservation equations written for finite control volume were integrated with properties of the water and nanofluids. The nanofluids studied and presented herein are Ai2O3, CuO, Fe3O4, and SiO2. The multiple flashing chamber process was studied under various conditions, including different solar radiation levels, brine flows and concentrations, and nanofluid concentrations as well as flashing chamber temperatures and pressures. Solar radiation levels were taken as 500 w/m2, 750 w/m2, 1000 w/m2, and finally, 1200 w/m2. The nanofluid volumetric concentrations considered varied from 1% to 20%. There is clear evidence that the higher the solar radiation, the higher the flashed flow produced. The results also clearly show that irreversibility is reduced by using nanofluid Ai2O3 at higher concentrations of 10% to 20% compared to water as base fluid. The highest irreversibility was experienced when water was used as base fluid and the lowest irreversibility was associated with nanofluid SiO2. The irreversibility increase depends upon the type of nanofluid and its thermodynamic properties. Furthermore, the higher the concentration (e.g., from 10% to 20% of Ai2O3), the higher the availability at the last flashing chamber. However, the availability is progressively reduced at the last flashing chamber. Finally, the predicted results compare well with experimental data published in the literature.


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