Computational Fluids Dynamics (CFD) is the essential method to study fluid physics. The CFD simulation of turbulence-heat transfer interactions assisting the design of heat exchanger surfaces with constructed roughness or micro-fins. For many practical problems, such as turbulence, CFD relies on the computer power, and the finer the grid resolutions is, the more accurate solutions may be possible. However, for analyses of small scale fluid physics, such as turbulence, the grid resolution could be prohibitively small, resulting prohibitively high computational cost (time to run the simulations). 

 

The revolutionary quantum computing may be used to solve complicated target turbulence research problems. Promisingly, quantum computers can solve problems exponentially faster than the classical computers in certain areas, such as optimization, and solving linear equations, etc. Unlike the classical computers which store information using bits represented by 0s or 1s, quantum computers use quantum bits, or qubits, to encode information as 0s, 1s, or both at the same time. This is called superposition of states. The superposition and the other quantum mechanical phenomena of entanglement are important characteristics of quantum computer, and they allow quantum computers to manipulate enormous combinations of states at once. The more qubits are used; the more combinations of states can exist at the same time. This is the key why quantum computers can solve problems exponentially faster in areas require exhausting search and combination. CFD simulation requires solving for linear equation sets, with matrix solvers and optimization algorithms, which is a perfect candidate for the quantum computing. Currently, IBM Q-Lab provides maximal 16 qubits quantum machine for public use, which is not enough for a practical full-size simulation. Therefore, a preliminary study of applying quantum computing to a simple CFD simulation is given. 

 

In this paper, a heat transfer problem was simulated by the state-of-art quantum computing technology. The problem was modeled by a linear system, Ax=b. The A matrix in the linear system is a Hermitian matrix. The linear system is then solved by using the HHL algorithm, which is a quantum algorithm to solve a linear system. The quantum circuit requires an Ancilla qubit, two clock qubits, one qubit for b, and a classical bit. The process of the HHL algorithm can be described as follows. Firstly, the qubit for b is initialized into the phase as desire. Secondly, the quantum phase estimation (QPE) is used to determine the eigenvalues of A and the eigenvalues are stored in clock qubits. Thirdly, a Pauli X-gate is used to invert eigenvalues and information is passed to the Ancilla bit to do controlled Pauli Y-rotation operation. Fourthly, revert the phase estimation, measure the clock qubits, and output the final results for x. The results were compared to the analytical solutions as well as traditional CFD solutions for validation. The errors of the quantum computing results were also analyzed to provide insights of the current capability of the quantum computing in CFD. 


Quantum CFD Simulations for Heat Transfer Applications

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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