Simulation Of Compressible Flows Research Articles

Preventing spurious pressure oscillations in split convective form discretization for compressible flows

This paper addresses issues in split convective form discretization in terms of the physical property of the pressure equilibrium to achieve physically-consistent, stable, and non-dissipative shock-free compressible flow simulations. Discrete pressure- and velocity-evolution equations are derived by using existing split convective form discretization, such as used in kinetic energy preserving (KEP) and kinetic energy and entropy preserving (KEEP) schemes. This analysis reveals that the existing KEP and KEEP schemes do not maintain the physical property of the pressure equilibrium due to the discretization of the internal energy convective term. The analysis also directly leads to the proposed split convective form discretization of the internal-energy convective term that strictly satisfies the pressure equilibrium at the discrete level. By applying the proposed discretization of the internal energy convective term to the existing KEEP scheme, this study shows that it is possible to satisfy the pressure equilibrium numerically with maintaining excellent kinetic energy and entropy preservation property. In numerical tests, the proposed scheme shows a superior numerical stability property without spurious pressure oscillations.

Toward fully conservative hybrid lattice Boltzmann methods for compressible flows

This article presents a new numerical scheme designed to solve for any scalar equation coupled with a lattice Boltzmann solver (in so-called hybrid methods). Its most direct application is solving an energy equation, in parallel with a lattice Boltzmann solver, dealing with mass and momentum conservation. The numerical scheme is specifically designed to compute the energy flux consistently with the mass and momentum flux (as is carried out, for instance, using Riemann solvers). This scheme effectively eliminates a major limitation of the current compressible hybrid lattice Boltzmann method, in which the energy conservation is tackled under a non-conservative form, leading to discretization errors on jump conditions across shocks. Combined with our recently presented pressure-based solver [G. Farag et al., “A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows,” Phys. Fluids 32(6), 066106 (2020)], the resulting hybrid lattice Boltzmann scheme is, to the authors’ knowledge, the first to numerically conserve mass, momentum, and total energy simultaneously.

Sequential coupling of thermal module into the reservoir simulator DMflow

In this work, we present a numerical framework for non-isothermal compositional compressible gas-water phase flow simulations in non-fractured and fractured porous media on structured and unstructured meshes. The framework is implemented as the simulator “DMflow”. The discretization of the mass conservation equations is based on the fully-implicit scheme and cell-centered finite-volume control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a lower dimensional fractured model. Similarly, the discretization of the energy equation is also based on the same method. The recent newly developed enthalpy model of CO2−CH4-H2S-N2-O2-brine system (Guo et al., 2019), which is validated within a wide temperature and pressure range, is used in the energy equation. Here, we present a sequential implicit method for the non-isothermal flow and avoid the simultaneous solution of the fluid flow primary variables and the temperature. We present the validation cases where the 1D and 2D results for non-isothermal carbon dioxide (CO2) injection into water obtained by the new implemented numerical framework are in agreement with the CMG-GEM. The simulation results of the injection of the CO2 into an aquifer shows the robustness of the method to produce gas phase behavior and temperature distribution in agreement with the literature. We also present a simulation case to demonstrate the capability of our simulator to model non-isothermal CO2 injection process into a fractured water saturated reservoir using an unstructured grid. The method is also then applied to simulate and compare the isothermal and the non-isothermal cases of injection of pure CO2 and impure CO2 into water reservoir with heterogeneity in porosity and permeability.

Immersed boundary conditions for hypersonic flows using ENO-like least-square reconstruction

In this study, we present an immersed boundary reconstruction method for the simulation of viscous compressible flows presenting strong discontinuities in the vicinity of the immersed body. The technique we propose is based on a weighted least-square reconstruction. Its major feature is that the weights are automatically adapted to the presence of a discontinuity within the least-square stencil by using a shock-sensor approach. In so doing, the reconstruction becomes ENO-like and mathematically consistent even in the presence of strong discontinuities. The objective of this paper is to demonstrate that it then becomes possible to use an immersed boundary method for the simulation of hypersonic flows and that it is robust, even for flows around complex geometries. To do so, two-dimensional compressible Navier-Stokes equations are solved to study canonical hypersonic flows and it is showed that the results are in good agreement with either experimental data and/or body-fitted approaches and that the impact of the immersed boundary technique on the overall spatial order of convergence is reasonable.

Compressible lattice Boltzmann methods with adaptive velocity stencils: An interpolation-free formulation

Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large velocity and temperature variations, it also strongly impacts the efficiency of the algorithm due to space interpolations that are required to get populations at grid nodes. To avoid this defect, the present work proposes new formulations of adaptive LBMs that do not rely anymore on space interpolations, hence drastically improving their parallel efficiency for the simulation of high-speed compressible flows. To reach this goal, the adaptive phase discretization is restricted to particular states that are compliant with the efficient “collide-and-stream” algorithm, and as a consequence, it does not require additional interpolation steps. The development of proper state-adaptive solvers with on-grid propagation imposes new restrictions and challenges on the discrete stencils, namely, the need for an extended operability range allowing for the transition between two phase discretizations. Achieving the minimum operability range for discrete polynomial equilibria requires rather large stencils (e.g., D2Q81, D2Q121) and is therefore not competitive for compressible flow simulations. However, as shown in this article, the use of numerical equilibria can provide for overlaps in the operability ranges of neighboring discrete shifts at acceptable cost using the D2Q21 lattice. Through several numerical validations, the present approach is shown to allow for an efficient realization of discrete state-adaptive LBMs for high Mach number flows even in the low-viscosity regime.

A Comparison of Interface Growth Models Applied to Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

Abstract Sophisticated numerical models that contain fluid interfaces rely upon interface evolution models to approximate the transition to turbulence near interfaces, in the presence of Rayleigh–Taylor (RTI) or Richtmyer–Meshkov (RMI) instability. Semi-analytical models have been developed in recent decades to predict the interface growth from an initial state into the nonlinear regime. Two of these models are considered in this study. They are the Goncharov and the z-models. Both of these interface models have strengths and weaknesses, which are examined here. Both of them have been implemented in the xRAGE compressible flow solver, which models fluid interfaces. The flow solver provides the fluids acceleration as a body force to the interface model. The purpose of such interface model is to evolve the early times of interface position as a subgrid model within a compressible flow simulation in order to then initialize a turbulence model. In this work, the interface models are assessed and compared for their evolution of RTI and RMI. The z-model performed better than the Goncharov model for all cases that were explored.

An accurate SPH Volume Adaptive Scheme for modeling strongly-compressible multiphase flows. Part 2: Extension of the scheme to cylindrical coordinates and simulations of 3D axisymmetric problems with experimental validations

The present work is dedicated to extending the strongly-compressible multiphase SPH Volume Adaptive Scheme (see [22]) from Cartesian to cylindrical polar coordinates for addressing axisymmetric problems. By omitting the gradient in the circumferential direction, an Axisymmetric-SPH model is developed. Three-dimensional axisymmetric problems including rising bubbles, expanding or collapsing bubbles are conveniently and efficiently simulated using the proposed Axisymmetric-SPH model. Contrary to the purely three-dimensional SPH model established in Cartesian coordinates, with the axisymmetric model, sufficient particle resolutions can be easily adopted to reach converged simulations of complex problems. Axisymmetric-SPH results are validated either using experimental data or other numerical results. In the Axisymmetric-SPH model, a convenient and effective way of avoiding singularity at the axis is presented. In addition, the Volume Adaptive Scheme (VAS), originally developed for compressible flow simulations with large volume variations in Cartesian coordinates, is shown to be a crucial tool to adjust particle volumes in the Axisymmetric-SPH model for all flow cases, including both weakly-compressible and strongly-compressible flows.

A sharp-interface immersed boundary method for simulating high-speed compressible inviscid flows

This paper presents a robust sharp-interface immersed boundary method for simulating inviscid compressible flows over stationary and moving bodies. The flow field is governed by Euler equations, which are solved by using the open source library OpenFOAM. Discontinuities such as those introduced by shock waves are captured by using Kurganov and Tadmor divergence scheme. Wall-slip boundary conditions are enforced at the boundary of body through reconstructing flow variables at some ghost points. Their values are obtained indirectly by interpolating from their mirror points. A bilinear interpolation is employed to determine the variables at the mirror points from boundary conditions and flow conditions around the boundary. To validate the efficiency and accuracy of this method for simulation of high-speed inviscid compressible flows, four cases have been simulated as follows: supersonic flow over a 15 ° angle wedge, transonic flow past a stationary airfoil, a piston moving with supersonic velocity in a shock tube and a rigid circular cylinder lift-off from a flat surface triggered by a shock wave. Compared to the exact analytical solutions or the results in literature, good agreement can be achieved.

Preconditioned gridless methods for solving three-dimensional Euler equations at low Mach numbers

In this paper, preconditioned gridless methods are developed for solving the three-dimensional (3D) Euler equations at low Mach numbers. The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations, which are discretized under the clouds of points distributed in the computational domain by using a gridless technique. The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning, which may fail to have convergence for flow simulations at low Mach numbers, therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper. An explicit four-stage Runge–Kutta scheme is first applied for time integration, and the lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence. Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform, and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing. The gridless clouds of both regular and irregular points are used in the simulations, which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries. Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature. The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally, for nearly incompressible flow simulations at low Mach numbers as well. The convergence of the implicit preconditioned gridless method, as expected, is much faster than its explicit counterpart.

An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation

High fidelity numerical simulation of compressible flow requires the numerical method being used to have both stable shock-capturing capability and high spectral resolution. Recently, a family of Targeted Essentially Non-Oscillatory (TENO) schemes is developed to fulfill such requirements. Although TENO has very low dissipation for smooth flow, it introduces a cutoff value CT to maintain the non-oscillatory shock-capturing property. As CT actually controls the dissipation property of TENO, the choice of CT for better shock-capturing capability also means higher dissipation for small structures. To overcome this, in this paper, a new local adaptive method is proposed for the choice of CT. By introducing a novel adaptive function based on the WENO smoothness indicators, CT is dynamically adjusted from 1.0×10−10 for lower dissipation to 1.0×10−4 for stable capturing of shock according to the smoothness of the reconstruction stencil. The numerical results of the new method are compared with those of the original TENO method and an adaptive TENO method in Fu et al. (2019) [49]. It reveals that the new method is capable of suppressing numerical oscillations near discontinuities while further improving the resolution of TENO at a low extra computational cost.

Control of cavity flow with acoustic radiation by an intermittently driven plasma actuator

In a cavity flow with acoustic radiation, self-sustained oscillations are controlled by a continuously or intermittently driven plasma actuator with elongated electrodes in the streamwise direction, which induces spanwise non-uniformity of the incoming boundary layer. To evaluate the control effects, wind tunnel experiments and compressible flow simulations were conducted. As indicated by sound pressure measurements at the fundamental frequency, the sound reduction level afforded by the intermittent control may be higher than that provided by the continuous control, although both have the same power consumption. In particular, the sound reduction was highest at a certain intermittent frequency (i.e., effective frequency) under a constant driving voltage and duty ratio. To clarify the mechanism for the influence of the intermittent frequency on the control effects, the time variation of the incoming boundary layer and cavity flow during the intermittent period was investigated. The oscillations remained weak under the control of the effective intermittent frequency, while the attenuation and amplification of the oscillations were repeated in the actuator-on and actuator-off durations, respectively, under the control of intermittent frequencies lower than the effective frequency. The amplification rate of the oscillations was found to be correlated with the quality factor of the radiated sound without control. The relationship between the effective frequency and characteristic time for this amplification is also discussed in this paper.

Hysteresis of aeroacoustic sound generation in the articulation of [s

A fricative consonant (e.g., [s]) is known to be pronounced by a turbulent jet flow inside the oral cavity. In this study, the effects of tongue motion on the aeroacoustic sound generation during the articulation of [s] were investigated through the large eddy simulation of compressible flow using a simplified vocal tract model. The walls of the simplified model were expressed using a volume penalization approach as an immersed boundary method, and the tongue geometry was ascended and descended from the position of /u/ to /s/ with tongue speeds of 40 mm/s, 60 mm/s, and 80 mm/s. The simulated acoustic pressure at a far-field sampling point was compared with previous experimental measurements, and the acoustic characteristics of the simulated sound reasonably agreed with those of the experiment. The overall acoustic amplitudes increased and decreased in accordance with tongue ascent and descent, and these transitions in amplitudes were almost the same for the different tongue speeds. Meanwhile, we found a hysteresis effect on the overall acoustic amplitudes between tongue ascent and tongue descent. This hysteresis was caused by the larger velocity fluctuations and vortices near the upper and lower teeth during tongue descent, and the results indicated that these flow differences occurred owing to the inertia of the turbulent flow structures and the aerodynamic pressures over the constriction of the vocal tract. This study suggests that these phenomena cause a delay in the sound generation of [s].

An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

In this paper, an efficient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible flow in porous media. The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of flow equation in original full-order space, and the discrete empirical interpolation method (DEIM) is applied to speed up the solution of Peng–Robinson equation of state in reduced-order subspace. The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reduced-order subspace, which not only preserves good prediction accuracy of full-order model, but also gains dramatic computational acceleration by multigrid and DEIM. Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method. In addition, the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng–Robinson equation of state is demonstrated and carried out in detail. Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors. The general acceleration is up to 50–60 times faster than that of standard semi-implicit method in two-dimensional simulations, but the average relative errors of numerical results between these two methods only have the order of magnitude 10−4–10−6%.

Large‐eddy simulation of subsonic turbulent jets using the compressible lattice Boltzmann method

SummaryThe lattice Boltzmann method (LBM) is a powerful technique for the computational modeling of a wide variety of single‐s and multiphase flows involving complex geometries. Although the LBM has been demonstrated to be effective for the solution of incompressible flow problems, there are limitations when this methodology is applied to the solution of compressible flows, especially for flows at high Mach numbers. In this article, we investigate strategies to overcome some of the limitations associated with the application of LBM to compressible flows. To this purpose, one of the key contributions of this study is the synthesis and integration of previous efforts concerning the formulation of LBM for the large‐eddy simulation (LES) of compressible turbulent flows in the subsonic flow regime. It is shown how certain limitations of applying the LBM to compressible flows can be addressed by using either a higher order Taylor series expansion of the Maxwell–Boltzmann equilibrium distribution function or using the Kataoka and Tsutahara (KT) LBM model formulation for compressible flows. The proposed LBM/LES methodology for compressible flows has been combined with the Kirchhoff integral formulation for computational aeroacoustics and used to simulate the flow and acoustic fields of compressible jet flows at high subsonic speeds with practical relevance for providing a better understanding of problems associated with jet noise. In this context, simulations of the physics associated with the jet flow and concomitant noise in the near‐ and far‐field regimes were conducted using the proposed framework of a compressible LBM/LES and Kirchhoff integral method. The results of the subsonic isothermal and nonisothermal jet flow simulations for the flow and acoustic fields have been compared with available numerical and experimental results with generally good to excellent agreement.

An L2-norm regularized incremental-stencil WENO scheme for compressible flows

For the simulation of compressible flow with a broadband of length scales and discontinuities, the WENO schemes using incremental stencil sizes other than uniform ones are promising for more robustness and less numerical dissipation. However, in smooth region, large weights may be assigned to smaller stencils due to the lack of high-order derivatives in the smoothness indicator compared with that of larger stencils, and may degrade the order accuracy especially in the region near critical points. In order to cope with this drawback, based on the stencil selection of WENO-IS [Wang et al., IJMF 104 (2018): 20–31], we propose an L2-norm regularized incremental-stencil WENO scheme in this paper. In order to avoid the above mentioned order degeneration, a new L2-norm regularization is introduced into the WENO weighting strategy by taking account the L2-norm error term. In addition, a high-order non-dimensional discontinuity detector is utilized as the regularization parameter for adaptive control. Then, a hybrid method is adopted to further improve the performance and the computational efficiency. A number of benchmark cases suggest that the present scheme achieves very good robustness and fine-structure resolving capabilities.

Rp‐adaptation for compressible flows

AbstractWe present a novel rp‐adaptation strategy for high‐fidelity simulations of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimizer to r‐adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements, respectively. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simulation. The adaptation workflow uses a sensor for both discontinuities and smooth regions that is cheap to calculate, but the framework is general and could be used in conjunction with other feature‐based sensors or error estimators. We demonstrate this proof‐of‐concept using two geometries in transonic and supersonic flow regimes. The method has been implemented in the open‐source spectral/hp element framework Nektar++, and adaptivity is performed by its dedicated high‐order mesh generation tool NekMesh. The results show that the proposed rp‐adaptation methodology is a reasonably cost‐effective way of improving simulation accuracy.

Analysis of flow and acoustic radiation in reed instruments by compressible flow simulation

Analysis of flow and acoustic radiation in reed instruments by compressible flow simulation

A centrifugal buoyancy formulation for Boussinesq‐type natural convection flows applied to the annulus cavity problem

SummaryTraditionally, the Boussinesq approximation is adopted for numerical simulation of natural convection phenomena where density variations are supposed negligible except through the gravity term of the momentum equation. In this study, a recently developed formulation based on a Boussinesq approximation is presented in which the density variations are also considered in the advection terms. Extending density‐variations to the advection terms captures centrifugal effects arising from both bulk enclosure rotation and within individual vortices, and thus more accurate results are expected. In this respect, the results of the proposed formulation are compared against the conventional Boussinesq simulations and weakly compressible approximation in the concentric horizontal annulus cavity. A new relation is established which maps the magnitude of the non‐Boussinesq parameter of incompressible flow to the corresponding relative temperature difference of a compressible flow simulation which is in agreement with the maximum allowed Gay‐Lussac number to avoid unphysical density values. For comparison purposes, variations of different thermo‐fluid parameters including average and local Nusselt number, entropy generation, and skin friction up to Ra = 105 are computed. Results obtained under the proposed approximation agree with the classical Boussinesq approximation up to Ra = 103 for large non‐Boussinesq parameter corresponding to the large relative temperature difference, but at Ra = 105, computed thermo‐fluid parameters via the two approaches are not identical which justifies the inclusion of large Gay‐Lussac number for convection dominated regime in natural convection problems.

Assessment of Cavitation Models for Compressible Flows Inside a Nozzle

This study assessed two cavitation models for compressible cavitating flows within a single hole nozzle. The models evaluated were SS (Schnerr and Sauer) and ZGB (Zwart-Gerber-Belamri) using realizable k-epsilon turbulent model, which was found to be the most appropriate model to use for this flow. The liquid compressibility was modeled using the Tait equation, and the vapor compressibility was modeled using the ideal gas law. Compressible flow simulation results showed that the SS model failed to capture the flow physics with a weak agreement with experimental data, while the ZGB model predicted the flow much better. Modeling vapor compressibility improved the distribution of the cavitating vapor across the nozzle with an increase in vapor volume compared to that of the incompressible assumption, particularly in the core region which resulted in a much better quantitative and qualitative agreement with the experimental data. The results also showed the prediction of a normal shockwave downstream of the cavitation region where the local flow transforms from supersonic to subsonic because of an increase in the local pressure.

Acceleration of NOISEtte Code for Scale-Resolving Supercomputer Simulations of Turbulent Flows

The present work is devoted to accelerating the NOISEtte code and lowering its memory consumption. This code for scale-resolving supercomputer simulations of compressible turbulent flows is based on higher-accuracy methods for unstructured mixed-element meshes and hierarchical MPI $$+$$ OpenMP parallelization for cluster systems with manycore processors. We demonstrate modifications of the underlying numerical method and its parallel implementation, which consist, in particular, in using a simplified approximation method for viscous fluxes and mixed floating-point precision. The modified version has been tested on several representative cases. The performance measurements and validation results are presented.