Author | Alvin Zhang and Onkar Sahni |
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Title | Finite Element Analysis of Boundary Layer Flows using a Mixed B-spline Setting on Hybrid Meshes |

Year | 2016 |

Journal | AIAA SciTech 2016 |

Pages | 1-14 |

Abstract | Numerical analysis of boundary layer flows requires careful approximations. For such flows, a semi-structured or hybrid boundary layer mesh is typically used, in which layered elements exist near the walls while the rest of the domain is filled with unstructured elements. In this work we exploit the underlying structure of the hybrid mesh to employ B-splines in the wall-normal direction in the layered portion of the mesh, while we use standard $C^0$ basis in the unstructured elements. Since the solution in the boundary layer region possesses large normal gradients along with high smoothness, use of B-splines (in the wall-normal direction) offer several advantages over a standard $C^0$ basis setting. Such a basis setting results in layered elements with wall-normal B-splines which are coupled with a standard $C^0$ basis in the wall-parallel directions and at the top of the layered portion. In this paper we first discuss the details of the current mixed basis setting and its implementation in a finite element code. We then present results for two manufactured boundary layer problems: one with a quartic profile and the other with an exponential profile. In the latter profile, we also consider cases which emulate a non-zero pressure gradient. In these problems, for the mixed basis setting with B-splines in the wall-normal direction, we observe the rate of convergence to be $p+1$ (in the $L_2$ norm of the solution error). |

DOI Link | 10.2514/6.2016-1099 |