Alternating lower-upper splitting iterative method and its application in CFD

Small time step is used to ensure convergence in the time-dependent method in computational fluid dynamics(CFD). An improved iteration method termed as the alternating lower-upper splitting (ALUS) iterative method was proposed to address the problem, in which the coefficient matrix was split into a lower and an upper triangular matrix. In each inner step, only two triangular matrices were solved by Thom asalgorithm, therefore the ALUS method is simple. Theorems were listed to ensure the ALUS method convergence.A linear equation problem and flow around the cylinder were used to illustrate the characteristic of the ALUS method.Theoretical analysis and numerical results both demonstrate the new method performs well for positive definite matrices. Withless amount of computational work, the CPU time can be greatlydiminished. Thus the new ALUS method is efficient and robust and it is applicable in CFD numerical simulation.