Journal Article10.2514/3.8159
An Implicit, Bidiagonal Numerical Method for Solving the Navier-Stokes Equations
E. von Lavante,W. T. Thompkins +1 more
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TL;DR: In this article, a predictor-corrector scheme was proposed to solve viscous, compressible problems in general coordinates for arbitrary two-dimensional geometries for arbitrary viscous flow regions.
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Abstract: In recent years, much progress has been made in solving fluid dynamical problems using finite difference methods. Solving inviscid compressible problems in two and three dimensions has become almost routine with many suitable methods, explicit or implicit, available. The problem of compressible, viscous flows in complicated geometries remains, however, a major challenge. Here fine mesh spacing in the viscous flow regions makes the explicit methods with their simple boundary conditions extremely costly. Existing implicit methods can make use of large time steps, but require inversions of large block tridiagonal matrices. A method recently developed by MacCormack eliminates this disadvantage by introducing a predictor-corrector scheme requiring the inversion of only block bidiagonal matrices. It is the aim of present work to extend this method to allow solution of viscous, compressible problems in general coordinates for arbitrary two-dimensional geometries.
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Citations
An Assessment of Numerical Solutions of the Compressible Navier-Stokes Equations
TL;DR: In this article, the authors defined the Jacobian of coordinate transformation as a Jacobian-of-coordinate transformation (JOTC) of a coordinate transformation with respect to specific heat conductivities.
56
An assessment of numerical solutions of the compressible Navier-Stokes equations
J. S. Shang
- 25 Jun 1984
TL;DR: In this paper, the authors defined the Jacobian of coordinate transformation as a Jacobian-of-coordinate transformation (JOTC) of a coordinate transformation with respect to specific heat conductivities.
36
A class of bidiagonal schemes for solving the Euler equations
TL;DR: A general class of second-order accurate bidiagonal schemes is proposed, containing a class of implicit schemes and one of semiexplicit schemes, and it is shown that these schemes are in- trinsically dissipative so that no artificial viscosity is necessary for linear stability.
27
Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations
TL;DR: In this article, an implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations without the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed.
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Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations
J. L. Lawrence,John C. Tannehill,Denny S. Chaussee +2 more
- 01 May 1984
Abstract: Application de la methode de differences finies implicite de MacCormack a la resolution des equations bidimensionnelles parabolisees de Navier-Stokes. Discussion des avantages et inconvenients de la methode; comparaison avec le schema de Beam-Warming en ce qui concerne la precision, la stabilite, le temps de calcul, la place en memoire et la facilite d'implementation. Application a un ecoulement laminaire hypersonique sur un coin de compression
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