Improvement of numerical schemes by incorporation of approximate solutions applied to rotating compressible flows
A method which reduces the truncation error in the numerical solution of differential equations by incorporating known. (asymptotic) approximations is described.The method was implemented in the solution by finite differences of rotating compressible or stratified axisymmetric flows in cylinders. This method, called in the sequel the “booster method”, is simple in principle and easy to implement in existing codes, while requiring only an insignificant amount of additional computer expenditure.
The “booster method” was applied in the case of second order ordinary differential equations and significant improvement of accuray resulted, especially in the presence of thin boundary layers. Application of this method to the above mentioned flow problems results in a substantial reduction of the number of computational points without loss of accuracy.
KeywordsTruncation Error Usual Method Compressible Flow Isothermal Flow Thin Boundary Layer
Unable to display preview. Download preview PDF.
- Bark, F.H., Bark, T.H.: “On Vertical Boundary Layers in a Rapidly Rotating Gas,” J. Fluid Mech., 78, 1976.Google Scholar
- Sakurai, T., Matsuda, T.: “Gasdynamics of a Centrifugal Machine”, J. Fluid Mech., 68, 1975.Google Scholar
- Toren, M., Solan, A.: “Laminar Compressible Flow over a Stationary Disk Confined in Rotating Cylinder,” J. Fluid Eng., 101, 1979.Google Scholar