  Quantum computational fluid dynamics (QCFD) offers a promising alternative to
classical computational fluid dynamics (CFD) by leveraging quantum algorithms
for higher efficiency. This paper introduces a comprehensive QCFD method,
including an iterative method "Iterative-QLS" that suppresses error in quantum
linear solver, and a subspace method to scale the solution to a larger size. We
implement our method on a superconducting quantum computer, demonstrating
successful simulations of steady Poiseuille flow and unsteady acoustic wave
propagation. The Poiseuille flow simulation achieved a relative error of less
than $0.2\%$, and the unsteady acoustic wave simulation solved a
5043-dimensional matrix. We emphasize the utilization of the quantum-classical
hybrid approach in applications of near-term quantum computers. By adapting to
quantum hardware constraints and offering scalable solutions for large-scale
CFD problems, our method paves the way for practical applications of near-term
quantum computers in computational science.
