Chimera grid technology with IPDG method
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摘要: 在内罚间断伽辽金(IPDG)方法框架内应用嵌套网格技术求解了二维可压缩Navier-Stokes方程。通过把黏性通量作为辅助变量实现了Navier-Stokes方程的降阶,继而用间断有限元方法进行离散得到空间半离散方程。时间推进采用Newton-Krylov隐式方法。利用库埃特流动精确解验证了该方法的精度。在此基础上,对包括有黏NACA0012翼型绕流、定常和非定常的圆柱绕流在内的若干典型测试算例开展数值模拟,进一步验证了该方法的鲁棒性和可靠性。在嵌套网格中应用了h型网格自适应技术用于提高激波分辨率,对NACA0012翼型无黏跨声速绕流开展数值模拟,结果表明:自适应之后的单元数相比无自适应时只增加了8.4%,但是激波分辨率得到了显著提高,激波附近的计算结果也与实验值符合得更好,从而验证了该方法的有效性。
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关键词:
- 二维可压缩Navier-Stokes方程 /
- 嵌套网格 /
- 间断伽辽金方法 /
- 内罚方法 /
- h型网格自适应技术
Abstract: An internal penalty discontinuous Galerkin (IPDG) method was developed to solve the 2-D (two-dimensional)compressible Navier-Stokes equations together with chimera grid technique.The viscous flux was introduced as an auxiliary variable to reduce the equation order.The semi-discrete equation was solved with the discontinuous Galerkin method,and time marching was carried out with the implicit Newton-Krylov method.The accuracy of above methods was validated with the Couette flow in comparison of the exact solution.In addition,several test cases including viscous NACA0012 airfoil,steady and unsteady flow around a circular cylinder were simulated to verify the robustness and feasibility of the present methods.Eventually,the h-grid adaptive technique was also adopted in chimera grid to improve the resolution of shock wave.The inviscid transonic flow case over NACA0012 airfoil was also simulated.Result showed that,the number of cells after adaptation only increased by 8.4% compared with that without adaptation,but the shock resolution was significantly improved,and the calculated results near the shock were in better agreement with the experimental values,thereby verifying the effectiveness of the method. -
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