An efficient large-scale mesh deformation method based on MPI/Open MP hybrid parallel radial basis function interpolation

An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation,the present method employs different surface points sets and influence radius for each volume point movement,accompanied with efficient geometry searching strategy.The deformed surface points,also called Control Points (CPs),are stored in each processor.The displacement of spatial points is interpolated by using only 20-50 nearest control points,and the local influence radius is set to 5-20 times the maximum displacement of control points.To shorten the searching time for the nearest control point clouds,an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique.Besides,an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications.Three 3D cases,including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements,are used to test the present mesh deformation method.The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 450 and more than 80% parallel efficiency with 1024 MPI processors.In addition,the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.

Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations

A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR(correction procedure or collocation penalty via reconstruction).The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure.In addition to being simple and economical,it unifies several existing methods including discontinuous Galerkin,staggered grid,spectral volume,and spectral difference.To discretize the diffusion terms,we use the BR2(Bassi and Rebay),interior penalty,compact DG(CDG),and I-continuous approaches.The first three of these approaches,originally derived using the integral formulation,were recast here in the CPR framework,whereas the I-continuous scheme,originally derived for a quadrilateral mesh,was extended to a triangular mesh.Fourier stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried out.Finally,results for the Navier-Stokes equations are shown to compare the various schemes as well as to demonstrate the capability of the CPR approach.