Quantum algorithm for the Navier-Stokes equations

A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented. The non-linearity of fluid flow equations is managed by using the stream function-vorticity formulation, while the lattice Boltzmann method (LBM) is utilized for solving the corresponding system of equations numerically. Following the nature of the lattice Boltzmann method, the proposed quantum algorithm consists of five major sections: initialization, collision, propagation, boundary condition implementation, and macros calculation. The collision and boundary condition step is quantumly implemented by applying the standard-form encoding approach, while the quantum walk procedure is applied for the propagation step. The algorithm is implemented by using IBM's quantum computing software development framework Qiskit, while for the verification purposes two-dimensional (2D) cavity flow is simulated and compared with classical code

Numeričko modeliranje brzotoka u krivini

Two-dimensional (2D) open-channel flow models for a steep chute with curvature in plane are developed. TVD McCormack and TVD MUSCL method have been used to facilitate an easy-to-use code. The performances of the numerical models have been assessed, and compared with experimental results.Prikazan je ravanski (2D) numerički model nejednolikog ustaljenog tečenja u brzotoku sa horizontalnom krivinom trase korita. Primenjene su metode McCormack i MUSCL, poboljšane sa TVD članom. Dobijeni rezultati numeričkih modela su upoređeni sa eksperimentalnim rezultatima

Numeričko modeliranje brzotoka u krivini

Two-dimensional (2D) open-channel flow models for a steep chute with curvature in plane are developed. TVD McCormack and TVD MUSCL method have been used to facilitate an easy-to-use code. The performances of the numerical models have been assessed, and compared with experimental results.Prikazan je ravanski (2D) numerički model nejednolikog ustaljenog tečenja u brzotoku sa horizontalnom krivinom trase korita. Primenjene su metode McCormack i MUSCL, poboljšane sa TVD članom. Dobijeni rezultati numeričkih modela su upoređeni sa eksperimentalnim rezultatima

Numeričko modeliranje brzotoka pri promeni pravca zida kanala

Two-dimensional (2D) open-channel flow models for contracting and expanding chutes are developed. TVD McCormack and TVD MUSCL method have been used to facilitate an easy-to-use code. The performances of the numerical models have been assessed, and the results compared with the analytical solutions.Razvijen je ravanski (2D) numerički model nejednolikog ustaljenog tečenja u brzotoku sa suženjem i proširenjem korita. Primenjene su metode MacCormack i MUSCL, poboljšane sa TVD članom. Dobijeni rezultati numeričkih modela su upoređeni sa analitičkim rešenjima

Numeričko modeliranje brzotoka pri promeni pravca zida kanala

Two-dimensional (2D) open-channel flow models for contracting and expanding chutes are developed. TVD McCormack and TVD MUSCL method have been used to facilitate an easy-to-use code. The performances of the numerical models have been assessed, and the results compared with the analytical solutions.Razvijen je ravanski (2D) numerički model nejednolikog ustaljenog tečenja u brzotoku sa suženjem i proširenjem korita. Primenjene su metode MacCormack i MUSCL, poboljšane sa TVD članom. Dobijeni rezultati numeričkih modela su upoređeni sa analitičkim rešenjima

Efficient parallelization of quantum basis state shift

Basis state shift is central to many quantum algorithms, most notably the quantum walk. Efficient implementations are of major importance for achieving a quantum speedup for computational applications. We optimize the state shift algorithm by incorporating the shift in different directions in parallel. This provides a significant reduction in the depth of the quantum circuit in comparison to the currently known methods, giving a linear scaling in the number of gates versus working qubits in contrast to the quadratic scaling of the state-of-the-art method based on the quantum Fourier transform. For a one-dimensional array of size $2^n$ for $n > 4$, we derive the total number of $15n + 74$ two-qubit $CX$ gates in the parallel circuit, using a total of $2n-2$ qubits including an ancilla register for the decomposition of multi-controlled gates. We focus on the one-dimensional and periodic shift, but note that the method can be extended to more complex cases

Mathematical modelling of flow and sediment transport – the Tisa dam case study

Velike brzine toka nizvodno od brane na rijeci Tisi kod Novog Bečeja (Srbija), uzrokovane velikom razlikom u vodostaju između uzvodnog i nizvodnog toka, dovode do erozije obale na desnoj strani neposredno nizvodno od pomoćnog preljeva, zbog čega je ugrožena i stabilnost brane. Imajući u obliku složenu interakciju parametara toka i pronosa nanosa na toj lokaciji, u radu se koristi pristup utemeljen na prostornom (3D) matematičkom modelu tečenja i pronosa nanosa koji je namijenjen za rješavanje takvih složenih procesa. Modelom je definirano optimalno rješenje koje udovoljava svim zahtjevima stabilnosti analiziranih građevina, pri čemu se uspoređuju rezultati dobiveni analizom postojećih uvjeta s rezultatom mjera koje se predlažu za rješavanje problema.High flow velocities downstream of the Tisa Dam at Novi Bečej (Serbia), produced by the large difference between water levels in the upstream and downstream reaches, cause bank erosion by the right bank immediately downstream of the emergency spillway, threatening stability of the dam itself. Due to complex interaction between the parameters of flow and sediment transport at the given location, an approach involving a spatial (3D) mathematical model of flow and sediment transport, aimed at solving such complex processes, is investigated in this paper. An optimum solution meeting all requirements for the stability of structures in question has been reached by the model, through comparison of the results generated by the existing conditions with the result provided by the measures proposed to fix the problems

Exploitation of Documented Historical Floods for Achieving Better Flood Defense

Establishing Base Flood Elevation for a stream network corresponding to a big catchment is feasible by interdisciplinary approach, involving stochastic hydrology, river hydraulics, and computer aided simulations. A numerical model calibrated by historical floods has been exploited in this study. The short presentation of the catchment of the Tisza River in this paper is followed by the overview of historical floods which hit the region in the documented period of 130 years. Several well documented historical floods provided opportunity for the calibration of the chosen numerical model. Once established, the model could be used for investigation of different extreme flood scenarios and to establish the Base Flood Elevation. The calibration has shown that the coefficient of friction in case of the Tisza River is dependent both on the actual water level and on the preceding flood events. The effect of flood plain maintenance as well as the activation of six potential detention ponds on flood mitigation has been examined. Furthermore, the expected maximum water levels have also been determined for the case if the ever observed biggest 1888 flood hit the region again. The investigated cases of flood superposition highlighted the impact of tributary Maros on flood mitigation along the Tisza River