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Temporal-adaptive Euler/Navier-Stokes algorithm for unsteady aerodynamic analysis of airfoils using unstructured dynamic meshes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kleb, William L. Williams, Marc H. Batina, John T. |
| Copyright Year | 1990 |
| Abstract | A temporal adaptive algorithm for the time-integration of the twodimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretiiation for the convective t ams and cenual differencing for the shear-stks and heat flux terms on an umtrucmed mesh of uiangles. The temporal adaptive algorithm is a time-accurate integration pmcedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an aweciahle computational savings can he achieved for both inviscid and viscous unsteady airfoil pmblems using unstructured meshe.% without degrading spatial or temporal accuracy. u Introduction In recent years. significant progress has been made in developing computational fluid dynamics methods for aerodynamic analysir!'l Much attention, for example. has been focused on developing methods for accelerating the m v a g e n c e to steady state of flow solvers using explicit time-lilarching!vl and less emphasis bas bea, given to improving algorithms which are used for the more computationallyintensive unsteady applications. The application of cumnt explicit time-marching schemes for unsteady problems is computationally expensive because of the very small time steps required for numerical stability. Adaptively refining meshes spatially is one method of * Rourrch Awisunt, School d Acmnrutiw and A m w i n . SNdml Mmba t Sen& Ream& M a . Utmbddy AamdyMnia E d . Sbwmnl t AsroFirtc Pmf-r, Mml d A m u t i c l md A-uti-. Man& AlAA AlAA D-iw Uividar. Saia Mmba AlAA P; This paper is declared a work of [he US. Government and is not subject to copyright protection in the United States. reducing the total number of cells and thus the cost of the computation. but in the context of unsteady flows, this still leaves the problem of a reslrictive global time step. For explicit timemarcbmg schanes, this restriction involves marching all of the cells at a time step usually dictated by the smallest of the cell volumes. The problem is magnified when using finer grids such as is the case for Navier-Stokes analysis. One method of avoiding this aspect of explicit schemes is to use implicit time marching. In m e caws. however, the time step necessary for accurately resolving the unsteadiness of the flow can easily make the implicit methods more expmsive than the explicit methods. Time-qccurate residual smoothing is anotha method which has been used to partially relax the stability restrictions of explicit time-marching rhemes!" This allows the solution to be marched with a larger time step. but increased compltational work is required. A more viable approafh to improve &e efficiency of explicit time-msrching schemes is through the use of temporal adaption. Temporal adoption can be thought of as time-accurate local time-stepping. With this procedure. each grid cell is integrated acmfding to the /mal flow physics and numerical stability. Time-aocuraey is maintained by bringing all cells to the same time level as determined by the step size of the largest cell. The purpose of this paper is to dexribe the development of a temporal adapxive algorithm applied to the time-integration of the unsteady twodimensional Euler or Navier-Stokes equations for the unsteady semdynamic analysis of airfoils. The flow solver involves an upwind flux-split spatial discretization for the convective tams and central differencing for the shear-stress and heat flux lerms on w unsmrtured mesh of triangles dong with temporal adaptive time integration. The paper describes the computational profedures that were developed, and gives examples and comparisons which assess the accuracy and efficiency of the capability. Analytical Dlrruwlon In this section, the laminar Navier-Stokes equations are presented including the numerical algnrilhm used for their solution. The algorithm is an extension of the Euler solver of Batina which uses either flux-vector or fluxdifference splitting for the spatial disaeti7stim and either explicit or implicit time-marching. formula Governing FAuatlonr The unsteady twodimensional laminar Navier-Stokes equations in Cartesian conrdinates can be written in mnservatinn law form as where the vectw of conserved variahles Q and the convective fluxm F and G are given hy |
| File Format | PDF HTM / HTML |
| DOI | 10.2514/6.1990-1650 |
| Alternate Webpage(s) | https://ia800300.us.archive.org/6/items/nasa_techdoc_19910001606/19910001606.pdf |
| Alternate Webpage(s) | https://doi.org/10.2514/6.1990-1650 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
