A NURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented $h$-Adaptivity (Communications in Computational Physics, 2022)
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 volumemethod was developed to solve the steady Euler equations, in which the desired highorder numerical accuracy was obtained for the equations imposed in the domain witha 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 computethe 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 introducedfor the steady Euler equations in a complex domain, and (iii) a goal-oriented a posteriorierror indicator is designed to further improve the efficiency of the algorithm towardsaccurately calculating a given quantity of interest. Numerical results obtained from avariety of numerical experiments with different flow configurations successfully showthe effectiveness and robustness of the proposed method.