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Volume 32, Issue 2
A NURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented $h$-Adaptivity

Xucheng Meng & Guanghui Hu

DOI: 10.4208/cicp.OA-2021-0143

Commun. Comput. Phys., 32 (2022), pp. 490-523.

Published online: 2022-08

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Steady Euler equations, NURBS-enhanced finite volume method, goal-oriented a posteriori error estimation, non-oscillatory k-exact reconstruction, point inversion.

  • AMS Subject Headings

76M12, 65N50, 35Q31, 65D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-490, author = {Meng , Xucheng and Hu , Guanghui}, title = {A NURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented $h$-Adaptivity}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0143}, url = {http://global-sci.org/intro/article_detail/cicp/20866.html} }
TY - JOUR T1 - A NURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented $h$-Adaptivity AU - Meng , Xucheng AU - Hu , Guanghui JO - Communications in Computational Physics VL - 2 SP - 490 EP - 523 PY - 2022 DA - 2022/08 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2021-0143 UR - https://global-sci.org/intro/article_detail/cicp/20866.html KW - Steady Euler equations, NURBS-enhanced finite volume method, goal-oriented a posteriori error estimation, non-oscillatory k-exact reconstruction, point inversion. AB -

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.

Meng , Xucheng and Hu , Guanghui. (2022). A NURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented $h$-Adaptivity. Communications in Computational Physics. 32 (2). 490-523. doi:10.4208/cicp.OA-2021-0143
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