Journal ArticleDOI
Implicit Algorithm for the Conservative Transonic Full-Potential Equation Using an Arbitrary Mesh
TLDR
In this paper, a new implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed.Abstract:
A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.read more
Citations
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Journal ArticleDOI
Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review
TL;DR: A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given in this article, along with a general mathematical framework and error analysis common to such coordinate systems.
Journal ArticleDOI
An analysis of finite-difference and finite-volume formulations of conservation laws
TL;DR: In this article, a coordinate-free formulation of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system, and the analysis considers general types of equations: potential, Euler, and Navier-Stokes.
Journal ArticleDOI
Viscous-inviscid interactions in external aerodynamics
R.C. Lock,B.R. Williams +1 more
TL;DR: In this article, the authors provide a physical background to the subject of viscous-inviscid interactions (VII) and provide a discussion of some relevant features of integral and differential methods for turbulent boundary layers.
Proceedings ArticleDOI
Fast, Conservative Algorithm for Solving the Transonic Full-Potential Equation
TL;DR: In this paper, a fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described, which uses an upwind bias of the density coefficient for stability in supersonic regions.
Journal ArticleDOI
Transonic flow computations using nonlinear potential methods
TL;DR: In this paper, the state of the art in transonic flow simulation using nonlinear potential methods for external aerodynamic applications is described and a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions.
References
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Journal ArticleDOI
Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies
TL;DR: In this paper, a method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of general multi-connected regions containing any number of arbitrarily shaped bodies is presented.
Journal ArticleDOI
Conservation equations of gasdynamics in curvilinear coordinate systems
TL;DR: In this article, a method of writing the conservation equations of gasdynamics in curvilinear coordinates which eliminates undifferentiated terms is presented. But the method is only applicable to orthogonal coordinates and not to general tensor transformations.
Journal ArticleDOI
Iterative solution of transonic flows over airfoils and wings, including flows at mach 1
TL;DR: In this article, a new method of calculating transonic flows based on a "rotated" difference scheme is described, which is suitable for the calculation of both two and three-dimensional flows without restriction on the speed at infinity and is well adapted to computer use.