**Author details**

René Steijl CFD Laboratory, School of Engineering, University of Glasgow, Glasgow, United Kingdom

\*Address all correspondence to: rene.steijl@glasgow.ac.uk

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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*Quantum Algorithms for Fluid Simulations DOI: http://dx.doi.org/10.5772/intechopen.86685*

[1] Nielsen MA, Chuang IL. Quantum

processing units. ACM Journal on Emerging Technologies in Computing

[9] Steijl R, Barakos GN. Coupled Navier-Stokes-molecular dynamics simulations using a multi-physics flow simulation framework. International Journal for Numerical Methods in Fluids. 2010;**62**:1081-1106. DOI:

[10] Steijl R, Barakos GN. Coupled Navier-Stokes/molecular dynamics simulations in nonperiodic domains based on particle forcing. International Journal for Numerical Methods in Fluids. 2012;**69**:1326-1349. DOI:

[11] Cercignani C. The Boltzmann Equation and its Applications. 2nd ed.

New York: Springer; 1987

[12] Vincenti WG, Kruger CH.

2nd ed. New York: Wiley; 1967

euromechflu.2008.01.001

PhysRevA.95.042343

[14] Fillion-Gordeau F, MacLean S, Laflamme R. Algorithm for the solution

of the Dirac equation on digital quantum computers. Physical Review A. 2017;**95**(4):042343. DOI: 10.1103/

Introduction to Physical Gas Dynamics.

[13] Alouges F, De Vuyst F, Le Coq G, Lorin E. The reservoir technique: A way to make Godunuv-type scheme zero to very low diffuse. Application to Colella-Glaz solver. European Journal of Mechanics-B/Fluids. 2008;**27**(6):643-664. DOI: 10.1016/j.

Systems. 2017;**1**(1):1-39. DOI:

10.1145/3007651

10.1002/fld.2641

10.1002/fld.2053

Information: 10th Anniversary Edition. 2nd ed. Cambridge, UK: Cambridge

Computation and Quantum

[2] Sinha S, Russer P. Quantum computing algorithm for

electromagnetic field simulation. Quantum Information Processing. 2010;**9**(3):385-404. DOI: 10.1007/

[3] Scherer A, Valiron B, Mau SC, Alexander S, van den Berg E, Chapuran TE. Concrete resource analysis of the quantum linear-system algorithm used to compute the electromagnetic scattering cross section of a 2D target. Quantum Information Processing. 2017;**16**(3):1-65. DOI: 10.1007/

[4] Xu G, Daley AJ, Givi P, Somma RS. Turbulent mixing simulation via a quantum algorithm. AIAA Journal. 2018;**56**(2):687-699. DOI: 10.2514/1.

[5] Steijl R, Barakos GN. Parallel evaluation of quantum algorithms for computational fluid dynamics. Computers & Fluids. 2018;**173**:22-28. DOI: 10.1016/.compfluid.2018.03.080

[6] Harrow AW, Hassidim A, Lloyd S. Quantum algorithm for linear systems of equations. Physical Review Letters.

2009;**15**:150502. DOI: 10.1103/ PhysRevLett.103.150502

[8] Britt KA, Humble TS. High-

performance computing with quantum

[7] Cao Y, Papageorgiou A, Petras I, Traub J, Kais S. Quantum algorithm and circuit design solving the Poisson equation. New Journal of Physics. 2013;**15**:013021. DOI: 10.1088/1367-2630/15/1/013021

University Press; 2010

s11128-009-0133-x

s11128-016-1495-5

J055896

**References**

*Quantum Algorithms for Fluid Simulations DOI: http://dx.doi.org/10.5772/intechopen.86685*
