Extending slide-slip mesh update method to finite volume method

Abstract For simulations of flows around rotating bodies, usually sliding mesh method or overset grid method is used. But both of them have to perform inter-mesh interpolation which introduces much numerical error and usually violates conservation. Shear-slip mesh update method (SSMUM) is another method for such flows. In each time step of SSMUM, a mesh slipping step follows a mesh deforming step to undo the deformation and results in a new mesh of good quality. Each vertex on the slipping interface can only move from one node to the next node in the circumference, which makes the interface always conformal and no need for inter-mesh interpolation. However, SSMUM didn't get enough attention in the community of finite volume method. In this paper, SSMUM is extended to cell center finite volume method. To guarantee conservation and obtain high order accuracy on a slipping interface, a remapping procedure is needed to transfer flow field from an old mesh to a new mesh. This was achieved by solving a linear convective PDE with one or two explicit steps, thus only resulting in little extra computing cost. Oscillating NACA0012 airfoil was simulated with the improved SSMUM. The results showed excellent agreement with the data by rigid rotating mesh. And the flow field was always smooth. It suggests that this improved SSMUM has advantages in getting conservative, smooth and high accuracy solutions for rotating problems.

[1]  Yuri Bazilevs,et al.  3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics , 2011 .

[2]  Marek Behr,et al.  The Shear-Slip Mesh Update Method , 1999 .

[3]  Meng-Sing Liou,et al.  A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics) , 1994 .

[4]  Ivan E. Sutherland,et al.  Reentrant polygon clipping , 1974, Commun. ACM.

[5]  Song Fu,et al.  Improvement to Patched Grid Technique with High-Order Conservative Remapping Method , 2011 .

[6]  H. Huynh,et al.  Accurate Monotonicity-Preserving Schemes with Runge-Kutta Time Stepping , 1997 .

[7]  Antony Jameson,et al.  Application of Dual Time Stepping to Fully Implicit Runge Kutta Schemes for Unsteady Flow Calculations , 2015 .

[8]  P. Thomas,et al.  Geometric Conservation Law and Its Application to Flow Computations on Moving Grids , 1979 .

[9]  Dingxi Wang,et al.  A complete rotor–stator coupling method for frequency domain analysis of turbomachinery unsteady flow , 2017 .

[10]  Steve Bryson,et al.  High-Order Central WENO Schemes for Multidimensional Hamilton-Jacobi Equations , 2013, SIAM J. Numer. Anal..

[11]  Tayfun E. Tezduyar,et al.  Shear-Slip Mesh Update in 3D Computation of Complex Flow Problems with Rotating Mechanical Components , 2001 .

[12]  Thomas Renaud,et al.  Computation of GOAHEAD configuration with Chimera assembly , 2012 .

[13]  Antony Jameson,et al.  Lower-upper implicit schemes with multiple grids for the Euler equations , 1987 .

[14]  Charbel Farhat,et al.  The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids , 2001 .

[15]  V. Parthasarathy,et al.  A fully automated Chimera methodology for multiple moving body problems , 2000 .

[16]  Kivanc Ekici,et al.  Harmonic Balance Analysis of Blade Row Interactions in a Transonic Compressor , 2010 .

[17]  Len G. Margolin,et al.  Second-order sign-preserving conservative interpolation (remapping) on general grids , 2003 .

[18]  Chi-Wang Shu,et al.  High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes , 2003, SIAM J. Sci. Comput..

[19]  J. Butcher.  Implicit Runge-Kutta processes , 1964 .

[20]  Rainald Löhner,et al.  Edge-based finite element scheme for the Euler equations , 1994 .

[21]  John C. Butcher,et al.  Integration processes based on Radau quadrature formulas , 1964 .

[22]  M. Shashkov,et al.  An efficient linearity-and-bound-preserving remapping method , 2003 .

[23]  A. Le Pape,et al.  Helicopter drag reduction by vortex generators , 2015 .