# Accession Number:

## ADA128737

# Title:

## Efficient ADI (Alternating Direction Implicit) and Spline ADI Methods for the Navier-Stokes Equations.

# Descriptive Note:

## Final rept. Jul-Sep 81,

# Corporate Author:

## DAYTON UNIV OH RESEARCH INST

# Personal Author(s):

# Report Date:

## 1983-02-01

# Pagination or Media Count:

## 40.0

# Abstract:

This report provides an improved Alternating Direction Implicit ADI technique as well as a high-order-accurate spline ADI method, for the numerical solution of steady two-dimensional incompressible viscous flow problems. The vorticity-stream function Navier-Stokes equations are considered in a general curvilinear coordinate system, which maps an arbitrary two-dimensional flow domain in the physical plane into a rectangle in the computational plane. The stream function equation is parabolized in time by means of a relaxation-like time derivative and the steady state solution is obtained by a time marching two-sweep ADI method, which requires to solve only linear 2 x 2 block-tridiagonal systems. The difference equations are written in incremental form windward differences are used for the incremental variable for stability, whereas central differences approximate the nonincremental terms for accuracy. Thus, at convergence, the solution is free of numerical viscosity and second-order-accurate. The high-order accurate spline ADI technique proceeds exactly in the same manner. In addition, at the end of each two sweep ADI cycle, the solution is corrected by means of a fifth-order-accurate solution is obtained, for the case of orthogonal coordinate systems. The validity and the efficiency of the present methods are demonstrated by means of their application to three test problems. Author

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Fluid Mechanics