Numerical Simulation of One-Dimensional Incompressible Transient Flow Using the Method of Characteristics (Midpoint Rectangular Formula)

The Method of Characteristics (Midpoint Rectangular Formula) for numerical simulation of one-dimensional incompressible transient flow is a computational fluid dynamics technique commonly applied in engineering practice. This method simulates parameter variations during object motion within fluid environments. The Method of Characteristics is a numerical approach based on flux-continuous invariants that transforms discontinuous parameters into continuous ones to solve nonlinear problems. The Midpoint Rectangular Formula represents a specific computational scheme within this method, offering relatively high computational accuracy. In practical implementations, this approach typically involves discretizing the governing partial differential equations along characteristic curves and applying finite difference approximations at intermediate grid points. Key algorithmic components include characteristic direction calculation, Riemann invariant tracking, and stability-preserving interpolation techniques. In engineering applications, the Method of Characteristics with Midpoint Rectangular Formula is frequently employed for simulating fluid transmission in pipeline systems and mixture transport behaviors in chemical engineering processes, where it efficiently handles wave propagation and transient phenomena through characteristic-based time marching algorithms.