Year: 2022
Author: Xucheng Meng, Guanghui Hu
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 490–523
Abstract
In [A NURBS-enhanced finite volume solver for steady Euler equations, X. C. Meng, G. H. Hu, J. Comput. Phys., Vol. 359, pp. 77–92], a NURBS-enhanced finite volume method was developed to solve the steady Euler equations, in which the desired high order numerical accuracy was obtained for the equations imposed in the domain with a curved boundary. In this paper, the method is significantly improved in the following ways: (i) a simple and efficient point inversion technique is designed to compute the parameter values of points lying on a NURBS curve, (ii) with this new point inversion technique, the $h$-adaptive NURBS-enhanced finite volume method is introduced for the steady Euler equations in a complex domain, and (iii) a goal-oriented a posteriori error indicator is designed to further improve the efficiency of the algorithm towards accurately calculating a given quantity of interest. Numerical results obtained from a variety of numerical experiments with different flow configurations successfully show the effectiveness and robustness of the proposed method.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0143
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 490–523
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Steady Euler equations NURBS-enhanced finite volume method goal-oriented a posteriori error estimation non-oscillatory k-exact reconstruction point inversion.