MULTI-DIMENSIONAL SQUARE WAVE EVALUATION AND SIMULATION EMPLOYING THE CUBIC INTERPOLATION PSEUDO-PARTICLE METHOD
DOI:
https://doi.org/10.11113/aej.v15.23676Keywords:
Cubic Interpolation pseudo-Particle (CIP), first order upwind, square wave, mean square error (MSE).Abstract
The Cubic Interpolation Pseudo-Particle (CIP) method is used in various papers to simulate different phenomena. It solves hyperbolic-type equations and is more efficient than a first-order upwind scheme. This verification gives one the future to apply CIP to other or more complex geometries. In this paper, we simulate the numerically square wave propagation based on characteristic equations, using the CIP method using 1D-CIP and 2D-CIP. Based on the idea that the wave field and its spatial derivative propagate along the same characteristic curves obtained from a hyperbolic differential equation. In this research, we simulate the numerical propagation of the acoustic wave based on characteristic equations, using the CIP method with two dimensions 1D-CIP & and 2D-CIP. In addition, provides several numerical simulation behaviors in demonstrating how the CIP can accurately model the propagation of acoustic waves without much numerical dispersion. Moreover, the mean square error displayed the superiority of 2D-CIP with 0.5% over 1D-CIP. However, the characteristic-based CIP method is a particularly effective way to handle wave propagation to tackle the fluid's dynamic challenges and give accuracy, managing nonlinearities, and flexibility, making it a useful tool in numerical analysis.
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