New Spatial Value Estimation Method for Curved Characteristic Line

Abstract

Numerical calculations are used in various situations. However, to achieve accurate numerical calculations, accuracy in the calculation method and initial values with high spatial resolution are necessary. Therefore, we propose a new method for estimating spatial values that considers characteristic theory but does not use interpolation. We consider the treatment of the curved characteristic line, which implies that the characteristic speed is altered locally. In the new method named averaging inverse characteristics method (AICM), the locally changing characteristic speed is averaged with the characteristic speed of the previous steps. We calculated the spatial values of the shock tube problem, described by the Euler equation, and examined the accuracy of the AICM by comparing the results of the inverse characteristics method (ICM) proposed in the previous study and the traditional interpolating methods. Compared to other methods, AICM reduced the error to less than 1/10 for all parameters. We determined from these results that the AICM accurately estimates the spatial distribution of problems where characteristic speed has significantly changed.