Present Hybrid Scheme Research Articles

An efficient hybrid WENO scheme with minimized dispersion and adaptive dissipation properties for compressible flows

A numerical scheme with good spectral properties is important for the simulation of compressible flows with various of length scales for fine flow scales resolving. The MDAD-HY scheme (Li et al., 2022) using a discontinuity detector and scale sensor achieves the minimized dispersion and adaptive dissipation property. However, the discontinuity detector is devised based on the ratio of the 1st-order and 2nd-order derivatives on two sides of the interface introducing excessive numerical cost. To address this issue, an efficient hybrid WENO scheme with minimized dispersion and adaptive dissipation properties is proposed in this work. Based on the characteristic-decomposition approach, the numerical flux of the present hybrid scheme is achieved by switching between the linear MDAD scheme and the MDAD-WENO scheme according to a new efficient non-dimensional discontinuity detector. The linear flux is reconstructed in a component-wise method to decrease the characteristic-projection operations. To further improve the spectral property of the present scheme, an adaptive parameter controlling the contribution of the optimal linear scheme according to the discontinuity indicator is introduced. Several benchmark test cases involving broadband of length scales and discontinuities are adopted to verify the efficiency and the high-resolution capability of the present scheme.

A unified stochastic particle method based on the Bhatnagar-Gross-Krook model for polyatomic gases and its combination with DSMC

Simulating hypersonic flow around a space vehicle is challenging because of the multiscale and nonequilibrium nature inherent in these flows. To effectively deal with such flows, a hybrid scheme combining the stochastic particle Bhatnagar-Gross-Krook (BGK) method with direct simulation Monte Carlo (DSMC) was developed recently, but only for monatomic gases (Fei et al. (2021) [29]). In this paper, the particle-particle hybrid method is extended to polyatomic gas flows. In the near continuum regime, employing the Ellipsoidal–Statistical BGK model proposed by Dauvois et al. (2021) [22] with discrete levels of vibrational energy, the stochastic particle BGK method for polyatomic gases is first established following the idea of the unified stochastic particle BGK (USP-BGK) scheme. It is proven to be of second-order accuracy in the fluid limit. After that, the USP-BGK scheme with rotational and vibrational energies is combined with DSMC to construct a hybrid scheme. The present hybrid scheme for polyatomic gases is validated with numerical tests of homogeneous relaxation, 1D shock structure and 2D hypersonic flows past a wedge and a cylinder. Compared to the other stochastic particle methods, the proposed hybrid scheme can achieve higher accuracy at a much lower computational cost. Therefore, it is a more efficient tool to study multiscale hypersonic flows.

A hybrid scheme coupling lattice Boltzmann method and finite-volume lattice Boltzmann method for steady incompressible flows

We present a new hybrid method coupling the adaptive mesh refinement lattice Boltzmann method (AMRLBM) and the finite-volume lattice Boltzmann method (FVLBM) to improve both the simulation efficiency and adaptivity for steady incompressible flows with complex geometries. The present method makes use of the domain decomposition, in which the FVLBM sub-domain is applied to the region adjacent to the walls, and is coupled to the lattice Boltzmann method (LBM) sub-domain in the rest of the flow field to enhance the ability of the LBM to deal with irregular geometries without sacrificing the high efficiency and accuracy property of the LBM. In the LBM sub-domain, a cell-centered lattice structure-based AMRLBM is used and, in the FVLBM sub-domain, the gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme-based FVLBM is adopted to reduce the numerical dissipation and enhance the efficiency of FVLBM. Moreover, not like the conventional LBM and Navier–Stokes equation solver-based hybrid schemes, the present hybrid scheme combines two kinds of lattice Boltzmann equation solvers, that is, AMRLBM and FVLBM, which makes the present scheme much simpler and better consistency than the conventional hybrid schemes. To assess the accuracy and efficacy of the proposed method, various benchmark studies, including the Kovasznay flow, the lid-driven cavity flow with Reynolds number Re=100, 400, and 1000, and the steady flow past a cylinder with Re=20 and 40, are also conducted. The numerical results show that the present scheme can be an efficient and reliable method for steady incompressible flows.

A Hybrid Targeted Eno-Thinc Scheme With a Modified BVD Algorithm and its Application in Stiff Detonation

This paper presents a new hybrid scheme which combines the fifth-order Targeted Essentially Non-Oscillatory (TENO) reconstruction and the tangent of hyperbola for interface capturing (THINC) reconstruction by using a modified boundary variation diminishing (MBVD) algorithm to select one of the two candidate reconstructions. The THINC scheme has a jump-like distribution can approximate a discontinuity well within a mesh cell with high fidelity. The original BVD algorithm is based on minimisation of jumps of reconstructed variables at cell interfaces in order to reduce the dissipation in numerical flux. The present MBVD algorithm minimises the dissipation terms of the HLL flux which includes jumps of both variables and fluxes at cell interfaces. A number of benchmark examples demonstrate that the MBVD algorithm is more robust than the original BVD algorithm. Applications in stiff detonation problems show that the present hybrid scheme can capture detonation fronts better than the single TENO scheme.

Solving combined economic emission dispatch model via hybrid differential evaluation and crow search algorithm

One of the major aspects regarding the operation and planning of a power system was to reduce the emission of pollutions and fuel costs in thermal power plants. This issue was resolved as an optimization crisis, where the reduction of emission of pollutions and fuel cost was done and it is known as the combined economic emission dispatch (CEED) problem. Various techniques were introduced for improving the performance of the power plants with respect to algorithm reliability, solution accuracy, global optimality, and convergence speed for resolving the CEED issues. Therefore, this work establishes a CEED approach for the smart grid system and resolves it by exploiting the hybridized concepts of the crow search algorithm (CSA) and differential evolution (DE). The hybridized model of the two well-known schemes is achieved by updating the solutions of both the schemes and merging them with the random searching model. Thus, the new approach is named as hybrid DE and CSA model. The CEED approach is subjected to reduce its cost and therefore, sufficient trade-off between the emission and economic costs could be sustained. The presented hybrid scheme is simulated on 3 diverse bus systems and its performance is evaluated over other state-of-the-art models in terms of CPU time and generation strategy.

New hybrid finite volume-thermal lattice Boltzmann method, based on multi relaxation time collision operator

Hybrid FVM-LBM schemes are developed in the past few years to use capabilities of both Navier-Stokes based finite volume method (FVM) and lattice Boltzmann method (LBM) to solve macro-meso multiscale problems. In this scheme, the major task is to develop some lifting relations that reconstruct distribution functions in LBM sub-domain from macroscopic variables and their derivatives. The macroscopic variables are computed using Navier-Stokes based FVM in macroscale sub-domain, while distribution functions are computed using LBM in mesoscale sub-domain. The pioneer works in this area used the single relaxation time (SRT) version of LBM. However, it is known that the numerical stability and accuracy of the multiple relaxation time (MRT) version of LBM is superior to the SRT one. Based on this fact, a new hybrid FVM-LBM scheme based on the MRT version of LBM for fluid flow simulation is proposed in our previous work. But, our previous hybrid scheme is limited to fluid flow problems. In the present research, some additional lifting relations are developed to extend the working area of our previous hybrid FVM-LBM (MRT) scheme to heat and mass transfer problems. The computational efficiency of the resulting hybrid method is proved by comparing its CPU time with those of LBM and Navier-Stokes based FVM for a sample meso-macro scale problem. Afterward, the new hybrid scheme is validated in two and three dimensions by solving three benchmark heat transfer problems. Additionally, to indicate the applicability of the present hybrid scheme in a meso-macro scale problem, three-dimensional heat transfer from a porous heat sink is simulated in pore scale. The fluid-solid conjugate heat transfer inside porous media is simulated using LBM, while the surrounding free fluid region is simulated using Navier-Stokes based FVM. The results indicate the superiority of the proposed new hybrid scheme over the previous ones.

A Low-Latency and Low-Power Hybrid Scheme for On-Chip Networks

Network-on-chip (NoC) has emerged as a vital factor that determines the performance and power consumption of many-core systems. This paper proposes a hybrid scheme for NoCs, which aims at obtaining low latency and low power consumption. In the presented hybrid scheme, a novel switching mechanism, called virtual circuit switching, is proposed to intermingle with circuit switching and packet switching. Flits traveling in virtual circuit switching can traverse the router with only one stage. In addition, multiple virtual circuit-switched (VCS) connections are allowed to share a common physical channel. Moreover, a path allocation algorithm is proposed in this paper to determine VCS connections and circuit-switched connections on a mesh-connected NoC, such that both communication latency and power are optimized. A set of synthetic and real traffic workloads are exploited to evaluate the effectiveness of the proposed hybrid scheme. The experimental results show that our proposed hybrid scheme can efficiently reduce the communication latency and power. For instance, for real traffic workloads, an average of 20.3% latency reduction and 33.2% power saving can be obtained when compared with the baseline NoC. Moreover, when compared with the NoC with virtual point-to-point connections (VIP), the proposed hybrid scheme can reduce the latency by 6.8% with the power decreasing by 11.3% averagely.

A hybrid boundary element-finite element approach to modeling plane wave 3D electromagnetic induction responses in the Earth

A novel hybrid boundary element-finite element scheme which is accelerated by an adaptive multi-level fast multipole algorithm is presented to simulate 3D plane wave electromagnetic induction responses in the Earth. The remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large-scale complicated geo-electromagnetic induction problems. To achieve this goal, first the Galerkin edge-based finite-element method (FEM) using unstructured meshes is adopted to solve the electric field differential equation in the heterogeneous Earth, where arbitrary distributions of conductivity, magnetic permeability and dielectric permittivity are allowed for. Second, the point collocation boundary-element method (BEM) is used to solve a surface integral formula in terms of the reduced electrical vector potential on the arbitrarily shaped air–Earth interface. Third, to avoid explicit storage of the system matrix arising from large-scale problems and to reduce the horrendous time complexity of the product of the system matrix with an initial vector of unknowns, the adaptive multilevel fast multipole method is applied. This leads to a matrix-free form suitable for the application of iterative solvers. Furthermore, a highly sparse problem-dependent preconditioner is developed to significantly reduce the number of iterations used by the iterative solvers.The efficacy of the presented hybrid scheme is verified on two synthetic examples against different numerical techniques such as goal-oriented adaptive finite-element methods. Numerical experiments show that at low frequencies, where the quasi-static approximation is applicable, standard FEM methods prove to be superior to our hybrid BEM–FEM solutions in terms of computational time, because the FEM method requires only a coarse discretization of the air domain and offers an advantageous sparsity of the system matrix. At radio-magnetotelluric frequencies of a few hundred kHz, the hybrid BEM–FEM scheme outperforms the FEM method, because it avoids explicit storage of the system matrices as well as dense volume discretization of the air domain required by FEM methods at high frequencies. In summary, to the best of our knowledge, this study is the first attempt at completely removing the air space for large scale complicated electromagnetic induction modeling in the Earth.

New scheme for introducing an oblique incidence plane wave to layered media in finite-difference time-domain

In the application of two-dimensional finite-difference time-domain (2D-FDTD) method to the analysis of scattering by an object embedded in layered media，the obliquely incident wave along the total field-scattered field (TF-SF) contains the incidence pulse and the reflected and multiple-reflected wave，which can not be introduced by use of the traditional method. To solve this problem，a hybrid scheme using different ways to treat the four TF-SF boundaries is presented. The modified 1D-FDTD including oblique incidence angle is used to treat the longitudinal side boundaries，which can produce the reflected and multiple-reflected wave to layered interface automatically. The longitudinal side boundaries are extended downwards，such that the TF-SF lower boundary is located in the perfectly matched layer (PML) completely，thus the transmission wave and scattered wave are both outward-going waves in the lowest PML layer，and are absorbed by PML. The TF-SF upper boundary is located in free space; the incidence wave along it is in fact a properly time-delayed duplication of the waveform at the corner of TF-SF upper longitudinal boundary. The computational results show the reliability and applicability of the presented hybrid scheme.

Hybrid lattice Boltzmann finite‐difference simulation of axisymmetric swirling and rotating flows

AbstractThe axisymmetric flows with swirl or rotation were solved by a hybrid scheme with lattice Boltzmann method for the axial and radial velocities and finite‐difference method for the azimuthal (or swirl) velocity and the temperature. An incompressible axisymmetric lattice Boltzmann D2Q9 model was proposed to solve the axial and radial velocities through inserting source terms into the two‐dimensional lattice Boltzmann equation. Present hybrid scheme was firstly validated by simulations of Taylor–Couette flows between two concentric cylinders. Then the benchmark problems of melt flow in Czochralski crystal growth were studied and accurate results were obtained. Numerical experiment demonstrated that present axisymmetric D2Q9 model is more stable than the previous axisymmetric D2Q9 model (J. Comp. Phys. 2003; 186(1):295–307). Hence, compared with the previous model, present numerical method provides a significant advantage in simulation melt flow cases with high Reynolds number and high Grashof number. Copyright © 2006 John Wiley & Sons, Ltd.

A hybrid spatial differencing scheme for discrete ordinates method in 2D rectangular enclosures

A hybrid spatial differencing scheme for the discrete ordinates method is proposed to predict radiation intensity in a two-dimensional rectangular enclosure. Since the hybrid scheme incorporates the strengths from the diamond scheme and the step scheme, and takes into consideration the characteristics of the medium, it is more accurate and yields more stable results. Several other spatial differencing schemes are examined to address the effect of numerical smearing (or false scattering). Predictions from the present hybrid scheme are compared to those of the other schemes for transparent, purely absorbing, purely scattering, and absorbing–emitting–isotropically scattering media. It is found that the proposed scheme predicts more stable and less smeared results than the others.

A hybrid central difference scheme for solid-state device simulation

The differences between the Scharfetter-Gummel and central difference schemes, applied to the drift and diffusion equations, are examined. It is shown that the differences between the two approximations lie essentially in numerical, or artificial diffusion that is introduced implicitly by the Scharfetter-Gummel scheme when the potential difference between grid points becomes excessive. Based on this observation, a hybrid central difference-artificial diffusion scheme is developed. It is shown that both the Scharfetter-Gummel and the present hybrid scheme have the same limiting forms at high and low fields, and it is demonstrated that both schemes yield similar results.