Engineering topics
Publications and source records attributed to Peraire, J..
This report summarizes the research undertaken, at Aeronautics Department of the Massachusetts Institute of Technology, during the approximately five year period, February 94 - March 99. This work is part of a larger effort aimed at providing a reliable fast turn around capability for the prediction of hypersonic flows over complete vehicle configurations.
A method for computing inviscid hypersonic flow over complex configurations using unstructured meshes is presented. The unstructured grid solver uses an edge{based finite{volume formulation. Fluxes are computed using a flux vector splitting scheme that is capable of representing constant enthalpy solutions. Second{order accuracy in smooth flow regions is obtained by linearly reconstructing the solution, and stability near discontinuities is maintained by locally forcing the scheme to reduce to first-order accuracy. The implementation of the algorithm to parallel computers is described. Computations using the proposed method are presented for a sphere-cone configuration at Mach numbers of 5.25 and 10.6, and a complex hypersonic re-entry vehicle at Mach numbers of 4.5 and 9.8. Results are compared to experimental data and computations made with established structured grid methods. The use of the solver as a screening tool for rapid aerodynamic assessment of proposed vehicles is described.
A description of the research work undertaken under NASA Research Grant NAGW-2962 has been given. Basic algorithmic development work, undertaken for the simulation of steady three dimensional inviscid flow, has been used as the basis for the construction of a procedure for the simulation of truly transient flows in three dimensions. To produce a viable procedure for implementation on the current generation of computers, moving boundary components are simulated by fixed boundaries plus a suitably modified boundary condition. Computational efficiency is increased by the use of an implicit time stepping scheme in which the equation system is solved by explicit multistage time stepping with multigrid acceleration. The viability of the proposed approach has been demonstrated by considering the application of the procedure to simulation of a transonic flow over an oscillating ONERA M6 wing.
The development of an algorithm for the solution of the compressible Euler equations at high Mach numbers on unstructured tetrahedral meshes is described. The basic algorithm is constructed in the form of a central difference scheme plus an explicit added artificial viscosity based upon fourth order differences of the solution. The stability of the solution in the vicinity of strong gradients is preserved by the incorporation of an additional artificial viscosity based upon a second order difference. Higher order accuracy is regained by using the ideas of flux corrected transport to limit the amount of added viscosity. The solution is advanced to steady state by means of an explicit multi-stage time-stepping method. The computational efficiency of the complete process is improved by incorporating an unstructured multigrid acceleration procedure. A number of flows of practical interest are analyzed to demonstrate the numerical performance of the proposed approach.
An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.
A practical solution algorithm for steady 3D Euler flows is presented. This algorithm employs coupling of a surface triangulator, an automatic tetrahedral mesh generator, an unstructured grid flow solver, and an error estimation procedure. The performance of the method is illustrated using a shock interaction problem in high Mach number flow over a swept circular cylinder.
The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.
The implementation of the finite element method on unstructured triangular grids is described and the development of centered finite element schemes for the solution of the compressible Euler equation on general triangular and tetrahedral grids is discussed. Explicit and implicit Lax-Wendroff type methods and a method based upon the use of explicit multistep timestepping are considered. In the latter case, the convergence behavior of the method is accelerated by the incorporation of a fully unstructured multigrid procedure. The advancing front method for generating unstructured grids of triangles and tetrahedra is described and the application of adaptive mesh techniques to both steady and transient flow analysis is illustrated.
A low storage, computationally efficient algorithm for the solution of the compressible Euler equations on unstructured tetrahedral meshes is developed. The algorithm takes the form of a centered scheme with the explicit addition of a high accuracy artificial viscosity and the solution is advanced to steady state by means of a multistage timestepping method. The side-based data structure which is employed enables a clear connection to be established between the proposed algorithm and upwind cell vertex schemes for unstructured meshes. The computational efficiency of the procedure is improved by incorporating an unstructured multigrid acceleration procedure. A number of flows of practical interest are analyzed to demonstrate the numerical performance of the proposed approach.
Adaptivity offers the possibility of using FEM for problems that are otherwise intractable. The solution algorithm is combined with an adaptive approach in which the unstructured portion of the grid is adaptively regenerated as the solution proceeds; the structured portion of the mesh is modified accordingly, to ensure both compatibility along the interface between the implicit and explicit element groups and increased resolution of the viscous layer. The approach offers significant computational savings in 3D simulations.
Explore the source record for details and available documents.
A general method is described for automatically discretizing, into unstructured assemblies of tetrahedra, the three-dimensional solution domains of complex shape which are of interest in practical computational aerodynamics. An algorithm for the solution of the compressible Euler equations which can be implemented on such general unstructured tetrahedral grids is described. This is an explicit cell-vertex scheme which follows a general Taylor-Galerkin philosophy. The approach is employed to compute a transonic inviscid flow over a standard wing and the results are shown to compare favorably with experimental observations. As a more practical demonstration, the method is then applied to the analysis of inviscid flow over a complete modern fighter configuration. The effect of using mesh adaptivity is illustrated when the method is applied to the solution of high speed flow in an engine inlet.
The solution of the equations governing steady laminar viscous flows on unstructured triangular meshes is addressed. The shortcomings of the standard adaptivity approaches for this class of problems are highlighted and a modified method based upon the combined use of mesh enrichment, mesh movement, and adaptive remeshing, is proposed. The behavior of the proposed scheme is demonstrated by applying it in the solution of compression corner flows.
This report gives a description of the work which has been undertaken during the second year of a three year research program. The objectives of the program are to produce finite element based procedures for the solution of the large scale practical problems which are of interest to the Aerothermal Loads Branch (ALB) at NASA Langley Research Establishment. The problems of interest range from Euler simulations of full three dimensional vehicle configurations to local analyses of three dimensional viscous laminar flow. Adaptive meshes produced for both steady state and transient problems are to be considered. An important feature of the work is the provision of specialized techniques which can be used at ALB for the development of an integrated fluid/thermal/structural modeling capability.
Over the past few years finite element based procedures for the solution of high speed viscous compressible flows were developed. The objective of this research is to build upon the finite element concepts which have already been demonstrated and to develop these ideas to produce a method which is applicable to the solution of large scale practical problems. The problems of interest range from three dimensional full vehicle Euler simulations to local analysis of three-dimensional viscous laminar flow. Transient Euler flow simulations involving moving bodies are also to be included. An important feature of the research is to be the coupling of the flow solution methods with thermal/structural modeling techniques to provide an integrated fluid/thermal/structural modeling capability. The progress made towards achieving these goals during the first twelve month period of the research is presented.
A method is described for generating unstructured meshes of triangles or tetrahedra for computational domains of complex geometrical shape. To illustrate the power of the approach, it is applied to the solution of flows past several complete aircraft configurations. The advocated approach allows for the natural incorporation of mesh adaptivity and this is demonstrated for both inviscid and viscous computations in two and three dimensions.
Mesh generation methods for Computational Fluid Dynamics (CFD) are outlined. Geometric modeling is discussed. An advancing front method is described. Flow past a two engine Falcon aeroplane is studied. An algorithm and associated data structure called the alternating digital tree, which efficiently solves the geometric searching problem is described. The computation of an initial approximation to the steady state solution of a given poblem is described. Mesh generation for transient flows is described.
An upwind cell-centered scheme for the solution of steady laminar viscous high-speed flows is implemented on unstructured two-dimensional meshes. The first-order implementation employs Roe's (1981) approximate Riemann solver, and a higher-order extension is produced by using linear reconstruction with limiting. The procedure is applied to the solution of inviscid subsonic flow over an airfoil, inviscid supersonic flow past a cylinder, and viscous hypersonic flow past a double ellipse. A detailed study is then made of a hypersonic laminar viscous flow on a 24-deg compression corner. It is shown that good agreement is achieved with previous predictions using finite-difference and finite-volume schemes. However, these predictions do not agree with experimental observations. With refinement of the structured grid at the leading edge, good agreement with experimental observations for the distributions of wall pressure, heating rate and skin friction is obtained.