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 - <p style="text-align: justify;">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.</p>