Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows  

作　　者：Luciano K.Araki Rafael B.de R.Borges Nicholas Dicati P.da Silva Chi-Wang Shu 

机构地区：[1]Department of Mechanical Engineering,Federal University of Paraná,Curitiba,81531-980,Paraná,Brazil [2]Mathematics and Statistics Institute,Rio de Janeiro State University,Rio de Janeiro,20550-900,Rio de Janeiro,Brazil [3]Department of Mechanical Engineering,State University of Maringá,Maringá,87020-900,Paraná,Brazil [4]Division of Applied Mathematics,Brown University,Providence,RI,02912,USA

出　　处：《Communications on Applied Mathematics and Computation》2024年第1期533-549,共17页应用数学与计算数学学报（英文）

基　　金：supported by the AFOSR grant FA9550-20-1-0055 and the NSF grant DMS-2010107.

摘　　要：Capturing elaborated flow structures and phenomena is required for well-solved numerical flows.The finite difference methods allow simple discretization of mesh and model equations.However,they need simpler meshes,e.g.,rectangular.The inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular meshes.High-resolution and high-order methods can capture elaborated flow structures and phenomena.They also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation concepts.We perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)schemes.Thus,we propose to solve a challenging engineering application without turbulence models.We aim to verify and validate recent high-resolution and high-order methods.To check the solver accuracy,we solved vortex and Couette flows.Then,we solved inviscid and viscous nozzle flows for a conical profile.We employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving Runge-Kutta.We showed the solver is high-order and captured elaborated flow structures and phenomena.One can see oblique shocks in both nozzle flows.In the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows.

关 键 词：HIGH-RESOLUTION COMPRESSIBLE NAVIER-STOKES Free-shock separation Nozzle flow 

分 类 号：O35[理学—流体力学]