A Method of the Lagrange Polynomial Interpolation with Weighting Factors for Reducing Computational Time

Abstract

This paper proposes a novel extrapolation method known as the Lagrange polynomial interpolation with weighting factors (LPI-WF) to determine initial guess values in each time step for solving equation systems of transient problems using iterative methods. The LPI-WF method is developed from the Lagrange polynomial interpolation to determine the direct extrapolation values and multiply them with the weighting factors. The weighting factors are calculated by considering the number of the previous time steps involved in the extrapolation and the duration between the present time step and the previous time steps. Thus, the LPI-WF method is proper for use with highorder temporal schemes. The key advantages of the LPI-WF method are that the computational time required to achieve the steady-state condition of the transient problems is reduced and the computation codes with the LPI-WF method is more stable than without the LPI-WF method at high time step values. A performance test of the LPI-WF method is carried out by comparing the computational time based on the “lid-driven cavity flow” problem for Reynolds numbers of 1000 and 5000. The test result shows that the computational time of the problem when the LPI-WF method is adopted can be reduced up to 10.46 % compared to the conventional method.