Conservative handling of arbitrary non-conformal interfaces using an efficient supermesh

This work presents a new and efficient strategy to handle non-conformal interfaces with the aim of assuring the conservation of fluxes in Finite Volume problems. A conservative interpolation is developed for general transport equations. Due to the arbitrary connectivity between the interfaces, the interpolations require flux-based weights defining a complex numerical stencil. In this context, a new method is proposed to simplify the coupling at the interface based on the construction of a simplified supermesh. Here, a supermesh is not completely defined, instead, the interface faces are logically duplicated (or multiplied) to generate a one-to-one connectivity between them. The simplified supermesh named pseudo-supermesh eliminates the interpolations and assures the conservation of fluxes based on the trivial connectivity. The area and the geometrical centroid of the new faces are redefined according to the overlapped sector of the original faces using the local supermeshing approach. Since the arbitrary polygons resulting from the face intersections are not generated and introduced into the mesh, computational cost and implementation efforts are saved. The proposed method is tested focusing on the conservation of fluxes and on the accuracy, showing conservation to machine precision and second order convergence as expected. In order to be able to solve large problems, the methodology is designed and implemented to be run in parallel architectures showing an excellent efficiency.

[1]  Sasa Kenjeres,et al.  On the improved finite volume procedure for simulation of turbulent flows over real complex terrains , 2015, J. Comput. Phys..

[2]  F. Piscaglia,et al.  Development of Fully-Automatic Parallel Algorithms for Mesh Handling in the OpenFOAM ® -2.2.x Technology , 2013 .

[3]  Z.J. WANG,et al.  Recent Development on the Conservation Property of Chimera , 2001 .

[4]  Man Mohan Rai,et al.  A relaxation approach to patched-grid calculations with the Euler equations , 1985 .

[5]  A. Lerat,et al.  Stable Conservative Multidomain Treatments for Implicit Euler Solvers , 1996 .

[6]  G. Taylor,et al.  Mechanism of the production of small eddies from large ones , 1937 .

[7]  M. Berger.  ON CONSERVATION AT GRID INTERFACES. , 1987 .

[8]  Enrico Rinaldi,et al.  Flux-conserving treatment of non-conformal interfaces for finite-volume discretization of conservation laws , 2015 .

[9]  G. Barakos,et al.  Sliding mesh algorithm for CFD analysis of helicopter rotor–fuselage aerodynamics , 2008 .

[10]  Man Mohan Rai,et al.  Navier-Stokes simulations of rotor-stator interaction using patched and overlaid grids , 1985 .

[11]  Ning Qin,et al.  Buffer Layer Method for Linking Two Non-Matching Multi-block Structured Grids , 2009 .

[12]  Patrick E. Farrell,et al.  Conservative interpolation between volume meshes by local Galerkin projection , 2011 .

[13]  Chia-Jung Hsu.  Numerical Heat Transfer and Fluid Flow , 1981 .

[14]  Luis Ramírez,et al.  New high-resolution-preserving sliding mesh techniques for higher-order finite volume schemes , 2015 .

[15]  Timothy J. Barth,et al.  The design and application of upwind schemes on unstructured meshes , 1989 .

[16]  Hrvoje Jasak,et al.  Development of a Generalized Grid Mesh Interface for Turbomachinery simulations with OpenFOAM , 2008 .

[17]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[18]  Sanjay Mathur.  Unsteady flow simulations using unstructured sliding meshes , 1994 .

[19]  Hrvoje Jasak,et al.  Automatic Mesh Motion with Topological Changes for Engine Simulation , 2007 .

[20]  Gaofeng Wang,et al.  An overset grid method for large eddy simulation of turbomachinery stages , 2014, J. Comput. Phys..

[21]  Rémi Abgrall,et al.  High‐order CFD methods: current status and perspective , 2013 .

[22]  F. Piscaglia,et al.  A Moving Mesh Strategy to Perform Adaptive Large Eddy Simulation of IC Engines in OpenFOAM , 2014 .

[23]  Peter Stansby,et al.  A simple sliding‐mesh interface procedure and its application to the CFD simulation of a tidal‐stream turbine , 2014 .

[24]  Ching Y. Loh,et al.  A Conservative Treatment of Sliding Interface for Upwind Finite Volume Methods , 2009 .

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

[26]  Matthew D. Piggott,et al.  Conservative interpolation between unstructured meshes via supermesh construction , 2009 .

[27]  Yibin Wang,et al.  Zipper layer method for linking two dissimilar structured meshes , 2013, J. Comput. Phys..

[28]  Wei Shyy,et al.  A study of finite difference approximations to steady-state, convection-dominated flow problems , 1985 .

[29]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .