Higher-order Time Integration Schemes for Aeroelastic Applications on Unstructured Meshes

Efficient techniques for computational aeroelasticity on unstructured meshes are investigated. These include the formulation of a fourth-order implicit Runge-Kutta time-integration scheme, a third-order backward-difference time-integration scheme, and a second-order backward-difference time-integration scheme for the coupled system of flow and structural equations. Strong coupling between the flow solution and structural equations is maintained by fully converging the fully coupled system at each time step or stage. The time-integration schemes are constructed such that discrete conservation is maintained in the flow solution in the presence of dynamically deforming meshes, by verifying the discrete geometric conservation law. Efficient multigrid solution techniques are devised for solving both the governing flow equations and the mesh motion equations, using the same agglomerated coarse levels for both problems. The flutter boundary prediction of the AGARD 445.6 wing is used to demonstrate the accuracy and efficiency of these techniques as well as the sensitivity of flutter boundary prediction to time-step size and temporal errors.

[1]  Dimitri J. Mavriplis,et al.  Unsteady Discrete Adjoint Formulation for Two-Dimensional Flow Problems with Deforming Meshes , 2008 .

[2]  D. Mavriplis,et al.  Mesh deformation strategy optimized by the adjoint method on unstructured meshes , 2007 .

[3]  Dimitri J. Mavriplis,et al.  Construction of the discrete geometric conservation law for high-order time-accurate simulations on dynamic meshes , 2006, J. Comput. Phys..

[4]  Zhi Yang,et al.  Achieving Higher-Order Time Accuracy for Dynamic Unstructured Mesh Fluid Flow Simulations: Role of the GCL , 2005 .

[5]  H. Bijl,et al.  High Order Time Integration For Fluid-Structure Interaction on Moving Meshes , 2005 .

[6]  Zhi Yang,et al.  Unstructured Dynamic Meshes with Higher-order Time Integration Schemes for the Unsteady Navier-Stokes Equations , 2005 .

[7]  Kwok Leung Lai,et al.  Application of Three-Dimensional Interfaces for Data Transfer in Aeroelastic Computations , 2004 .

[8]  Wei Shyy,et al.  Time Dependent RANS Computation for an Aeroelastic Wing , 2004 .

[9]  Dimitri J. Mavriplis,et al.  Higher order time integration schemes for the unsteady Navier-Stokes equations on unstructured meshes , 2002 .

[10]  Hester Bijl,et al.  Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow , 2002 .

[11]  K. Nakahashi,et al.  Unstructured dynamic mesh for large movement and deformation , 2002 .

[12]  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 .

[13]  D. Mavriplis.  An assessment of linear versus non-linear multigrid methods for unstructured mesh solvers , 2001 .

[14]  Her Mann Tsai,et al.  Calculation of Wing Flutter by a Coupled Fluid-Structure Method , 2001 .

[15]  W. K. Anderson,et al.  Recent improvements in aerodynamic design optimization on unstructured meshes , 2001 .

[16]  Charbel Farhat,et al.  On the significance of the geometric conservation law for flow computations on moving meshes , 2000 .

[17]  Timothy J. Baker,et al.  Dynamic adaptation for deforming tetrahedral meshes , 1999 .

[18]  S. Pirzadeh,et al.  Large-Scale Parallel Unstructured Mesh Computations for Three-Dimensional High-Lift Analysis , 1999 .

[19]  Charbel Farhat,et al.  On the implicit time integration of semi‐discrete viscous fluxes on unstructured dynamic meshes , 1999 .

[20]  Charbel Farhat,et al.  Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes , 1999 .

[21]  Dimitri J. Mavriplis,et al.  AIAA 99 – 0537 LARGE-SCALE PARALLEL UNSTRUCTURED MESH COMPUTATIONS FOR 3 D HIGH-LIFT ANALYSIS , 1999 .

[22]  Dimitri J. Mavriplis,et al.  On Convergence Acceleration Techniques for Unstructured Meshes , 1998 .

[23]  C. Farhat,et al.  Torsional springs for two-dimensional dynamic unstructured fluid meshes , 1998 .

[24]  P. Tallec,et al.  Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity , 1998 .

[25]  Dimitri J. Mavriplis,et al.  Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows , 1998 .

[26]  D. Mavriplis.  Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes , 1997 .

[27]  Charbel Farhat,et al.  Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations , 1996 .

[28]  V. Venkatakrishnan,et al.  A UNIFIED MULTIGRID SOLVER FOR THE NAVIER-STOKES EQUATIONS ON MIXED ELEMENT MESHES , 1995 .

[29]  V. Venkatakrishnan,et al.  IMPLICIT METHOD FOR THE COMPUTATION OF UNSTEADY FLOWS ON UNSTRUCTURED GRIDS , 1995 .

[30]  Dimitri J. Mavriplis,et al.  MULTIGRID TECHNIQUES FOR UNSTRUCTURED MESHES , 1995 .

[31]  Juan J. Alonso,et al.  Fully-implicit time-marching aeroelastic solutions , 1994 .

[32]  M Lee Elizabeth,et al.  Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics , 1993 .

[33]  H. J. Cunningham,et al.  Wing-flutter calculations with the CAP-TSD unsteady transonic small-disturbance program , 1989 .

[34]  J. Batina.  Unsteady Euler airfoil solutions using unstructured dynamic meshes , 1989 .

[35]  E C Yates,et al.  AGARD Standard Aeroelastic Configurations for Dynamic Response I - Wing 445.6 , 1988 .

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

[37]  R. N. Desmarais,et al.  Interpolation using surface splines. , 1972 .