Computers & Fluids最新文献

Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection–diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other. Specifically, we solve the linear partial differential equation with a Quantum Linear Systems Algorithm (QLSA) based on the Harrow–Hassidim–Lloyd method and a Variational Quantum Algorithm (VQA), for resolutions that can be encoded using up to 6 qubits, which corresponds to $N=64$ grid points on the unit interval. Both algorithms are hybrid in nature, i.e., they involve a combination of classical and quantum computing building blocks. The QLSA and VQA are solved as ideal statevector simulations using the in-house solver QFlowS and open-access Qiskit software, respectively. We discuss several aspects of both algorithms which are crucial for a successful performance in both cases. These are the accurate eigenvalue estimation with the quantum phase estimation for the QLSA and the choice of the algorithm of the minimization of the cost function for the VQA. The latter algorithm is also implemented in the noisy Qiskit framework including measurement noise. We reflect on the current limitations and suggest some possible routes of future research for the numerical simulation of classical fluid flows on a quantum computer.

Recently, the general synthetic iterative scheme (GSIS) has been proposed to find the steady-state solution of the Boltzmann equation in the whole range of gas rarefaction, where its fast-converging and asymptotic-preserving properties lead to the significant reduction of iteration numbers and spatial cells in the near-continuum flow regime. However, the efficiency and accuracy of GSIS have only been demonstrated in two-dimensional problems with small numbers of spatial cells and discrete velocities. Here, a large-scale parallel computing strategy is designed to extend the GSIS to three-dimensional flow problems, including the supersonic flows which are usually difficult to solve by the discrete velocity method. Since the GSIS involves the calculation of the mesoscopic kinetic equation which is defined in six-dimensional phase-space, and the macroscopic high-temperature Navier–Stokes–Fourier equations in three-dimensional physical space, the proper partition of the spatial and velocity spaces, and the allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys to improving the overall computational efficiency. These factors are systematically tested to achieve optimal performance, up to 100 billion spatial and velocity grids. For hypersonic flows around the Apollo reentry capsule, the X38-like vehicle, and the space station, our parallel solver can obtain the converged solution within one hour.

Immersed boundary method (IBM) is widely used for simulating flow in complex geometries using structured grids. However, this entails a disadvantage when simulating internal flows through curved and bent tubes. The presence of grids outside the fluid domain leads to the wastage of memory and computational overheads. Here, we propose a multi-block-multi-mesh framework to capture the complex geometry using multiple grid blocks fitted close to the body, reducing excess grids. This also has the advantage of using different and non-uniform grid spacing in different blocks. The reduction of the grid enables encompassing bigger caseloads on a single GPU. The solver is accelerated on GPU using OpenACC, compared to sequential CPU simulations, and speedup is presented. The speedup obtained is comparable to that of large multicore systems. The framework is extensively validated for straight artery with axisymmetric stenosis and bileaflet mechanical heart valve with axisymmetric sinus. This framework then models complex arterial flows like stenosed aorta, patient-specific branched aorta, bileaflet mechanical heart valve with Valsalva sinus and aorta, and lastly, patient-specific iliac aortic aneurysm. This framework achieves a significant reduction in GPU memory requirement for complex arterial models, enabling us to perform direct numerical simulation (DNS) of the stenosed aorta and mechanical heart valve cases in a single GPU.

We propose third-order A-WENO finite difference schemes that are based on the recently introduced first-order numerical schemes in [N. K. Garg et al., Journal of Computational Physics, 407(2020)] for the systems of compressible Euler equations of gas dynamics. The convective components of these schemes (fluxes), both in one- and multi-dimensions, are free from complicated Riemann solvers. Third-order characteristic-wise WENO-Z interpolations are employed to obtain the third-order point values required for the numerical fluxes. To demonstrate the robustness and accuracy of the resulting schemes, we compare the numerical results with local Lax–Friedrichs (LLF) and Harten–Lax–van Leer (HLL) fluxes on various one- and two-dimensional examples. The obtained results outperform LLF and HLL fluxes in terms of enhancing the resolution of contact waves, especially near isolated steady and moving contact discontinuities, as well as in accurately resolving high-frequency waves in one dimension (1-D) and the small-scale structures in two dimensions (2-D).

An artificial compressibility approach is proposed to compute the solution of the compressible equations in the low Mach number limit, in closed domain with moving boundaries. The low Mach number stiffness is reduced by introducing an artificial sound speed, much lower than the physical one. This allows to avoid both the acoustic time step restriction and the loss of accuracy of classical compressible solvers, without solving a Poisson equation for the pressure or using the time-implicit discretization of the Turkel-type preconditioning technique. Moreover the proposed formulation involves the conservative variables plus the dynamic pressure, which facilitates the implementation of the approach in classical CFD codes for compressible flows. The numerical experiments presented show that the approach is both accurate and CPU efficient.

It is attempted earnestly to elucidate the mechanism of collision and drainage of liquid mass around the spherical substrate suspended within the hollow cylinder using Gerris open-source code by employing Volume of Fluid (VOF) methodology. Various influencing parameters, namely, sphere-to-droplet diameter ratio $\left(D_s/D_o\right)$, Weber number$\left(We\right)$, Ohnesorge number $\left(Oh\right)$, and Bond number$\left(Bo\right)$ are employed to observe the drainage mechanism through the constricted path. The pattern of the interfacial morphology of droplet collision and drainage mechanism is presented using numerical contours. It is important to mention herein that the droplet undergoes several important stages like collision, cap formation, engulfment, drainage, and pinch-off. The passage between the sphere and the cylinder is sufficiently wider at a lower value of $D_s/D_o$ due to which the liquid mass is drained out completely without any hindrance. The drainage process becomes considerably faster at a higher $We$ compared to a lower $We$. In addition, the flow of liquid mass through the passage gets delayed at a greater $Oh$ than a lower $Oh$ assuming a given value of $We$ and $D_s/D_o$. The liquid drop requires less time to pass through the constricted path at lower $Bo$ for a given value of $D_s/D_o$ and $We$. We have also attempted to quantify the drainage of liquid volume passes through the passage, which is denoted as $\left(Q^{*}=Q/Q_o\right)$. One can notice the increasing pattern of $Q/Q_o$ with continuous progress of time stamp for all cases of $D_s/D_o$