High-speed Compressible Flows Research Articles

Quantum algorithm for nonlinear Burgers' equation for high-speed compressible flows

Quantum algorithm for nonlinear Burgers' equation for high-speed compressible flows

A filtered Rankine–Hugoniot method for consistent stochastic particle LES-FDF modelling of combustion in high-speed flows

A new model consistency scheme based on the filtered form of the Rankine–Hugoniot (R–H) relation is developed for hybrid Eulerian/Lagrangian Large Eddy Simulation-Filtered Density Function (LES-FDF) methods to model combustion in compressible high-speed flows. The approach particularly pertains to the evolution of the FDF stochastic Lagrangian particles in enthalpy space, accounting for the subgrid effects in the filtered R–H relation to ensure stable solutions and model consistency with the total energy field solved by an Eulerian compressible finite volume scheme. An analytical form of the subgrid term appearing in the filtered R–H relation is derived and it is shown to have a significant effect on the ability to accurately produce the post-shock thermochemical state. Subsequently, two novel numerical schemes are proposed based on either a modelled subgrid scale kinetic energy or a relaxation over a physical timescale. In testing for 1D normal shock cases, the former approach is found to be strongly dependent on the filter width and Mach number, while the latter approach produces consistent results. The relaxation method is further tested for a turbulent 3D shock tube case and a 1D detonation case and found to produce numerically consistent and accurate temperature and species fields. It is shown that the subgrid term is critical for accurately and consistently predicting the temperature fields in both cases and for achieving the correct detonation structure involving a leading shock and autoignition in the second case.Novelty and significance statementLES-FDF methods have not been widely used for high-speed combusting flows with strong shocks. Such flows are common in aerospace combustors and accurate modelling of these is essential for their optimisation, especially with rapid transition to alternative fuels. The first novelty is the development of a filtered Rankine–Hugoniot model to ensure energy consistency between the Eulerian LES and the FDF modelled through Lagrangian particles. The inclusion of a subgrid kinetic energy term in the Lagrangian particle energy equation is shown to be essential for producing consistent solutions and accurate prediction of thermodynamics states through discontinuities. This subgrid term is not closed and, therefore, the second novelty lies in proposing a practical numerical scheme which accounts for it. The consistent model and numerical scheme is validated in canonical shock tube and detonation cases.

A particle-resolved direct numerical simulation method for the compressible gas flow and arbitrary shape solid moving with a uniform framework

Compressible particle-resolved direct numerical simulations (PR-DNS) are widely used in explosion-driven dispersion of particles simulations, multiphase turbulence modelling, and stage separation for two-stage-to-orbit vehicles. The direct forcing immersed boundary method (IBM) is a promising method and widely applied in low speed flow while there is few research regarding compressible flows. We developed a novel IBM to resolve supersonic and hypersonic gas flows interacting with irregularly shaped multi-body particle. The main innovation is that current method can solve the interaction of particles and high-speed fluids, particle translation and rotation, and collision among complex-shaped particles within a uniform framework. Specially, high conservation and computation consumption are strictly satisfied, which is critical for resolving the high speed compressible flow feature. To avoid the non-physical flow penetration around particle surface, an special iterative algorithm is specially derived to handle the coupling force between the gas and particles. The magnitude of the velocity difference error could be reduced by 6–8 orders compared to that of a previous method. Additionally, aerodynamic force integration was achieved using the momentum equation to ensure momentum conservation for two-phase coupling. A high-efficiency cell-type identification method for each step was proposed, and mapping among LPs and cells was used again to select the immersed cells. As for the collision force calculation, the complex shape of a particle was represented by a cloud of LPs and the mapping of LPs and cells was used to reduce the complexity of the algorithm for contact searching. The repetitive use of the mapping relationship could reduce the internal memory and improve the efficiency of the proposed algorithm. Moreover, various verification cases were conducted to evaluate the simulation performance of the proposed algorithm, including two- and three-dimensional moving and motionless particles with regular and complex shapes interacting with high-speed flow. Specifically, an experiment involving a shock passing through a sphere was designed and conducted to provide high-precision data. The corresponding results of the large-scale numerical simulation agree well with those obtained experimentally. The current method supports flow simulations at a particle-resolved scale in engineering.

Experimental and numerical study on the high-speed gas-solid nozzle erosion of choke manifold material in high pressure and high production gas well

High pressure difference, high flow rate, and high sand content in throttling manifolds of high-pressure and high-production gas wells make the problems of high-speed gas-solid erosion wear especially prominent. The failure of the throttling manifold is frequent, which is easy to induce overflow, kick, and blowout accidents, aggravates well-controlled risks, and brings safety risks. Therefore, according to ASTM G76–2013, this paper adopts the gas-solid nozzle erosion test method and air jet erosion test rig. The high speed (107 m/s-49 m/s) gas-solid nozzle erosion test of 30CrMo alloy steel was carried out under different inlet pressures (0.06 MPa–0.15 MPa) and impact Angle (15°-90°), and the erosion rate of 30CrMo alloy steel under different experimental conditions was obtained. The erosion rate equation of 30CrMo alloy steel suitable for high-speed solid particle impact is established. Based on the results of erosion experiments, the optimal particle motion model for high-speed compressible flow is constructed. Combined with the discrete phase model (DPM) and gas-solid two-phase coupling calculation method, a three-dimensional CFD erosion model of the “reduced-tuber-nozzle-erosion cavity” was established. The erosion simulation of the gas-solid nozzle of 30CrMo alloy steel, a throttling manifold material, was carried out at different impact angles (15°-90°) and inlet pressure (0.06 MPa–0.15 MPa), and the distribution characteristics of the flow field, particle movement trajectory, impact velocity distribution, and slip characteristics were revealed. The accuracy and reliability of the CFD erosion model and simulation results have been validated by test data.

An averaged mass correction scheme for the simulation of high subsonic turbulent internal flows using a lattice Boltzmann method

This paper addresses the simulation of internal high-speed turbulent compressible flows using lattice Boltzmann method (LBM) when it is coupled with the immersed boundary method for non-body-fitted meshes. The focus is made here on the mass leakage issue. The recent LBM pressure-based algorithm [Farag et al. Phys. Fluids 32, 066106 (2020)] has shown its superiority on classical density-based algorithm to simulate high-speed compressible flows. Following our previous theoretical work on incompressible flows [Xu et al. Phys. Fluids 34, 065113 (2022)], we propose an averaged mass correction technique to mitigate mass leakage when simulating high-Mach-number compressible flows. It is adapted to deal here with a density, which is decoupled from the zero-moment definition. The simulations focus on two generic but canonical configurations of more complex industrial devices, the straight channel at different angles of inclination at Mach numbers (Ma) ranging from 0.2 to 0.8, and the National Aeronautics and Space Administration Glenn S-duct at Ma = 0.6. The present results show that mass leakage can be a critical issue for the accuracy of the solution and that the proposed correction technique effectively mitigates it and leads to significant improvements in the prediction of the solution.

High speed flows with particles on demand: Boundary conditions

The particles on demand (PonD) method is a new kinetic theory model that allows for simulation of high speed compressible flows. While the standard lattice-Boltzmann method is limited by a fixed reference frame, significantly reducing the range of Mach numbers, PonD takes advantage of adaptive reference frames to get rid of the restrictions of standard LB and is able to simulate flows at high speeds and with large temperature variation. Previously, PonD has been shown to be a viable alternative for simulation of flows with strong discontinuities and for detonation modelling. However, treatment of flows with complex boundaries has been lacking. Here, we present PonD augmented with a non-equilibrium extrapolation based boundary condition. We present several compressible test cases such as shock-vortex interaction in the Schardin’s problem and supersonic flow over a two-dimensional cylinder at Mach numbers up to 5. We observe that the results agree well with literature, paving the way for a kinetic theory based approach for simulating compressible flows in realistic scenarios.

A new open-source library based on novel high-resolution structure-preserving convection schemes

This work develops a new finite volume convection scheme and open-source library for convection-dominated problems on unstructured grids. The formulated reconstruction operators can realize high-resolution and structure-preserving properties by adjusting numerical dissipation and anti-dissipation errors in a unified normalized-variable diagram. Then, this work develops a new open-source library based on the devised schemes within one of the most widely used general-purpose open-source software whose solution quality is intrinsically limited by the low accuracy of the conventional total variation diminishing schemes. The performance of the new library is first verified by some fundamental problems including pure advection and inviscid Euler equations. The numerical results of the accuracy tests show that the developed interpolation library can significantly reduce numerical errors with a minor increased computational cost compared with the conventional second-order schemes. The complex profile advection test demonstrates that the new library can offer an improved structure-preserving property that gives essentially oscillation-free solutions and preserves the structures of the passive transported scalar. Furthermore, the robustness of the new library is validated by compressible high-speed flow simulations with irregular geometries. Thus, this work presents a new library of high-resolution structure-preserving schemes for the accurate and efficient discretization of the convection term which plays an essential role in a wide range of computational fluid dynamics. The source code of the new scheme and library are released via DOI:10.5281/zenodo.8399000.

Cartesian grid-based hybrid NS-DSMC methodology for continuum-rarefied gas flows around complex geometries

This work presents a coupled numerical methodology, based on a hybrid Navier-Stokes (NS) and Direct Simulation Monte Carlo (DSMC) method, for high-speed compressible gas flows—involving a combination of continuum and rarefied flow regions. Implementation details of coupling cycle are presented along with the validation and performance studies for three cases (Mach number M a 1 = 3.38 , 6.5 and 9) of normal shock waves in argon and three cases (Inlet pressure pin = 1.0 atm, 0.5 atm and 0.1 atm) of flow through a micro-scale convergent-divergent (CD) nozzle. In comparison with our DSMC method-based solutions in the complete domain, the hybrid NS-DSMC method solutions achieve almost similar accuracy in a substantially reduced computational time—44% to 50% for the normal shock problem and 67% to 85% for the micro-scale CD nozzle problem. For the first time in literature, the hybrid NS-DSMC method is presented as a Cartesian-grid method, which is becoming popular nowadays.

Hybrid Lattice Boltzmann Approach for Simulation of High-Speed Flows

A lattice Boltzmann approach utilizing hybrid lattices for accurate simulation of high-speed transonic (TS) flows is presented in this study. Single-layer lattice models, such as D3Q19, are computationally efficient with low numerical dissipation, but are limited to simulate weakly compressible flows within subsonic Mach regime. Multilayer lattice models, such as D3Q33, are capable of simulating thermal and high-speed compressible flows in TS Mach regime, but suffer from a higher numerical dissipation and higher computational cost. To take full advantages of these two types of lattices, a simulation domain is divided into two regions, high-subsonic (HS) flow regions to be solved by single-layer lattices and TS flow regions to be solved by multilayer lattices. The interface connecting the HS and TS flow regions are represented by double-sided surfels to realize smooth flow transition and ensure satisfaction of fundamental conservation laws. The hybrid lattice Boltzmann approach is stable and robust, and it allows multiple HS/TS flow regions with arbitrary shapes. Extensive validation studies demonstrate that the proposed approach is capable of obtaining accurate aerodynamic prediction of flows with a wide range of Mach numbers, and preserving the low numerical dissipation advantage of single-layer lattices in aeroacoustic computations.

Development of three-dimensional rotated lattice Boltzmann flux solver for the simulation of high-speed compressible flows

A three-dimensional (3D) Rotated Lattice Boltzmann Flux Solver (RLBFS) is proposed and analyzed with matrix-based linear stability theory for simulating compressible flows in a wide range of Mach numbers. The 3D RLBFS applies the finite volume method to discrete the Navier-Stokes equations and evaluates its fluxes at each cell interface. To improve numerical stability, the convective fluxes are obtained in a hybrid way by using the D1Q4 lattice Boltzmann model in two perpendicular directions decomposed by the outer normal vector of each cell interface. The viscous fluxes are computed in a conventional way using the second-order central scheme. The stability performance and order accuracy of the proposed 3D RLBFS are examined by using the matrix-based stability theory and L2 errors on different meshes respectively. It is shown that the 3D RLBFS is stable even at high Mach number and has the second-order accuracy in space. The reliability and capability of the proposed method is further evaluated by simulating several challenging compressible flow problems, including subsonic flow over the DLR-F4, transonic flow over the ONERA M6 wing, supersonic flow around NACA0012 wing, hypersonic flow over the Viking lander capsule, hypersonic flow over a hemisphere and hypersonic flow around a blunt nose double cone. The obtained numerical results are in good agreement with experimental and/or numerical data published in the literature, indicating that the present method provides a reliable and effective tool for simulating practical three-dimensional compressible flow problems in aeronautics and astronautics.

A multi-relaxation-time discrete Boltzmann model of compressible nonequilibrium reactive flows

A multi-relaxation-time discrete Boltzmann model (DBM) is proposed for compressible nonequilibrium reactive flows. The uniform discrete Boltzmann equations are the governing equations of the discrete distribution functions that describe the reactive system. On the right-hand side of the discrete Boltzmann equations, the reaction terms calculated by the inverse matrix method are used to couple chemical reactions and multi-physical fields naturally. Numerical tests show that the DBM is suitable for premixed, non-premixed and partially premixed reactive systems, and is also capable of high-speed compressible reactive flows.

An accurate and practical numerical solver for simulations of shock, vortices and turbulence interaction problems

Numerical simulations of high-speed compressible flows remain challenging in engineering as the appearance of shock waves poses difficulties for high-resolution schemes as well as explicit large eddy simulation methods. Therefore, in this work, we propose a practical numerical solver for simulations of shock-vortex and shock-turbulence problems with the implicit large eddy simulation approach and newly developed low-dissipative schemes. In order to handle the multi-scale raised in the shock-vortex and shock-turbulence problems, it is required that the flow solver can simultaneously solve the large-scale flow structures such as shock waves with numerical oscillation-free, the resolvable flow structures above the grid scale with low-dissipation, and the under-resolve isotropic sub-grid scale with numerical stability. To this end, a low-dissipative, structure-preserving scheme with rigorously adjusted numerical dissipation is employed in the proposed solver. The structure-preserving property of this scheme can ensure that the large-scale structure is solved without numerical oscillations and the low-dissipative property of this scheme can produce high-resolution results for the resolvable flow scales. Moreover, the sub-grid scale is solved and stabilized by the inherent numerical dissipation in the shock-capturing scheme. The proposed numerical solver is then applied to simulate a wide range of shock-vortex and shock-turbulence interaction problems including supersonic planar jets, transonic flows past a deep cavity and impingement of a supersonic jet on a cone mounted on a flat plate. A comparison is also made with the solver using conventional total variation diminishing schemes. The numerical results of the supersonic planar jet have demonstrated that the proposed solver can resolve the small-scale structure such as Kelvin–Helmholtz instability involved in shock and shear layer with high-resolution. Through the results of transonic flow past a deep cavity and comparisons with the experimental data, it is verified that the proposed solver can reproduce the turbulence statistical data. Furthermore, the proposed solver resolves the complex turbulent fluid mechanical phenomena in the impingement of a supersonic jet on a cone, which demonstrates the proposed solver can robustly handle irregular geometry. The proposed solver also enjoys simplicity without using the explicit sub-grid scale model and involving the complexity of very high-order schemes. Thus, this work provides an accurate and practical numerical solver for shock-vortex and shock-turbulence problems in high-speed flows.

Adaptative finite element simulation of unsteady turbulent compressible flows on unstructured meshes

The simulation of high-speed turbulent compressible flows using Large Eddy Simulation (LES) combined with the Characteristic-Based Split scheme (CBS) and a mesh adaptation strategy is presented in this work. A compressible dynamic Smagorinsky model is employed for the compressible LES model and the CBS scheme is employed in a Finite Element Method (FEM) context for space and time discretization using unstructured meshes. An accurate mesh adaptation scheme is frequently applied along the simulation including mesh refinement, mesh coarsening, edge or face swapping and a vertex smoothing technique in order to control the interpolation error and the mesh size. A feature-based error estimation is employed considering multi-scale and multi-metric intersection in order to capture turbulence effects. Two and three-dimensional applications are evaluated in order to investigate the capabilities of the present approach for evaluating external turbulent and compressible aerodynamics problems. The turbulent transonic flow around a circular cylinder in 2D and 3D domains and the turbulent supersonic flow past a blunt cylinder-flare model are investigated. Aerodynamic coefficients, frequency analysis and pressure distributions are compared against experimental data and other numerical simulations.

A discrete unified gas kinetic scheme on unstructured grids for viscid compressible flows and its parallel algorithm

<abstract><p>In this paper, we present a discrete unified gas kinetic scheme (DUGKS) on unstructured grids for high-speed viscid compressible flows on the basis of double distribution function (the density and the total energy distribution functions) Boltzmann-BGK equations. In the DUGKS, the discrete equilibrium distribution functions are constructed based on a D2Q17 circular function. In order to accelerate the simulation, we also illustrate a corresponding parallel algorithm. The DUGKS is validated by two benchmark problems, i.e., flows around the NACA0012 airfoil and flows past a circular cylinder with the Mach numbers range from 0.5 to 2.5. Good agreements with the referenced results are observed from the numerical results. The results of parallel test indicate that the DUGKS is highly parallel scalable, in which the parallel efficiency achieves $ 93.88\% $ on a supercomputer using up to $ 4800 $ processors. The proposed method can be utilized for high-resolution numerical simulation of complex and high Mach number flows.</p></abstract>

A parallel discrete unified gas kinetic scheme on unstructured grid for inviscid high-speed compressible flow simulation

The discrete unified gas kinetic scheme (DUGKS) is a recently devised approach to simulate multiscale flows based on the kinetic models, which also shows distinct features for continuum flows. Most of the existing DUGKS are sequential or based on structured grids, thus limiting their scope of application in engineering. In this paper, a parallel DUGKS for inviscid high-speed compressible flows on unstructured grids is proposed. In the framework of the DUGKS, the gradients of the distribution functions are calculated by a least-square method. To parallelize the method, a graph-based partitioning method is employed to guarantee the load balancing and minimize the communication among processors. The method is validated by several benchmark problems, i.e., a two-dimensional (2D) Riemann problem, 2D subsonic flows passing two benchmark airfoils, a 2D regular shock reflection problem, 2D supersonic flows (Mach numbers are 3 and 5) around a cylinder, an explosion in a three-dimensional (3D) box, a 3D subsonic flow around the Office National d'Etudes et de Recherches Aérospatiales M6 wing, a 3D hypersonic flow (Mach number is 10) around a hemisphere, and a supersonic flow over the Northrop YF-17 fighter model. The numerical results show good agreement with the published results, and the present method is robust for a wide range of Mach numbers, from subsonic to hypersonic. The parallel performance results show that the proposed method is highly parallel scalable, where an almost linear scalability with 93% parallel efficiency is achieved for a 3D problem with over 55 × 106 tetrahedrons on a supercomputer with up to 4800 processors.

Discrete Boltzmann modeling of high-speed compressible flows with various depths of non-equilibrium

The non-equilibrium high-speed compressible flows present wealthy applications in engineering and science. With the deepening of Thermodynamic Non-Equilibrium (TNE), higher-order non-conserved kinetic moments of the distribution function are needed to capture the main feature of the flow state and the evolution process. Based on the ellipsoidal statistical Bhatnagar–Gross–Krook model, Discrete Boltzmann Models (DBMs) that consider various orders of TNE effects are developed to study flows in various depths of TNE. In numerical tests, DBMs including the first up to the sixth order TNE effects are demonstrated. Specifically, at first, the model's capability to capture large flow structures with zeroth-order TNE effects in two types of one-dimensional Riemann problems is demonstrated. The ability to capture large flow structures with first-order TNE effects is also shown in the Couette flow. Then, a shock wave structure given by Direct simulation Monte Carlo is used to verify the model's capability to capture fine structures at the level of the mean free path of gas molecules. Furthermore, we focus on the TNE degree of two colliding fluids mainly decided by two parameters: the relaxation time τ and relative speeds Δu of two fluids. Consequently, three numerical tests for flows with various depths of TNE are constructed. Due to any definition of the TNE strength is dependent on the perspective of investigation, we propose to use a N-component vector STNE to describe the TNE system from N perspectives. As specific applications, we use a three-component vector STNE=(τ,Δu,Δ2*) to roughly characterize three cases for numerical tests in this work. Then, we check the system TNE behavior from the perspective of the xx component of the TNE quantity, viscous stress Δ2*. It is found that, for the first two cases, at least up to the second-order TNE effects, i.e., the second-order terms in Knudsen number in the CE expansion, should be included in the model construction, while for the third case, at least up to the third-order TNE effects should be included. Similar to Δ2*, three numerical tests for flows in various depths of Δ3,1* are constructed. It is found that from the perspective of Δ3,1,x*, for case 1 and case 3, at least up to the second-order TNE effects should be required, while for case 2, the first-order TNE effects are enough. These findings demonstrate that the inadequacy of focusing only on the few kinetic moments appearing in Navier–Stokes increases with the degree of discreteness and deviation from thermodynamic equilibrium. Finally, a two-dimensional free jet is simulated to indicate that, to obtain satisfying hydrodynamic quantities, the DBM should include at least up to the third-order TNE effects. This study is meaningful for the understanding of the TNE behavior of complex fluid systems and the choice of an appropriate fluid model to handle desired TNE effects.

Development and verification of a high-speed compressible reactive flow solver in OpenFOAM

This paper proposes a newly developed density-based compressible solver called DCRFoam on a basis of OpenFOAM platform for simulating detonation phenomena with detailed chemical kinetics. It employs AUSM+-up scheme to determine the convective fluxes and a four steps low storage Runge-Kutta time integration method for time integration. A total variation diminishing (TVD) and symmetrical flux limiter sgva is implemented for interpolation process. Also, the dynamic mesh adaptation method is applied to refine or coarsen the computational mesh dynamically since the resolution requirements of supersonic combustion are localized. The numerical solver has been validated systematically with many numerical and experimental results reported in the literature, including those from non-reacting cases (Sod’s shock tube problem, two-dimensional shock/cylinder interaction) to reacting flow cases (the ignition sequence in a shock tube, oblique detonation wave (ODW) initiating process and detonation propagating in a bifurcated channel). The results obtained by current schemes are compared with original central upwind Kurganov-Noelle-Petrova (KNP) scheme in official OpenFOAM. The corresponding result demonstrates the robustness and accuracy of the current solver.

A new paradigm of dissipation-adjustable, multi-scale resolving schemes for compressible flows

The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for capturing strong shock waves. In this work, we develop a new paradigm of dissipation-adjustable, shock capturing scheme to resolve multi-scale flow structures in high speed compressible flow. The new scheme employs a polynomial of n-degree and non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) functions of m-level steepness as reconstruction candidates. These reconstruction candidates are denoted as PnTm. From these candidates, the piecewise reconstruction function is selected through the boundary variation diminishing (BVD) algorithm. Unlike other shock-capturing techniques, the BVD algorithm effectively suppresses numerical oscillations without introducing excess numerical dissipation. Then, an adjustable dissipation (AD) algorithm is designed for scale-resolving simulations. This novel paradigm of shock-capturing scheme is named as PnTm−BVD−AD. The proposed PnTm−BVD−AD scheme has following desirable properties. First, it can capture large-scale discontinuous structures such as strong shock waves without obvious non-physical oscillations while resolving sharp contact, material interface and shear layer. Secondly, the numerical dissipation property of PnTm−BVD−AD can be effectively adjusted between n+1 order upwind-biased scheme and non-dissipative n+2 order central scheme through a simple tunable parameter λ. Thirdly, with λ=0.5 the scheme can recover to n+2 order non-dissipative central interpolation for smooth solution over all wavenumber, which is preferable for solving small-scale structures in DNS as well as resolvable-scale in explicit LES. Finally, the under-resolved small-scale can be solved with the dissipation adjustable algorithm through the so-called implicit LES (ILES) approach. Through simulating benchmark tests involving multi-scale flow structures and comparing with other central-upwind schemes, the superiority of the proposed scheme is evident. For instance, the simulation results of the supersonic planar jet show that PnTm−BVD−AD schemes can achieve competitive results as Pn+2Tm−BVD schemes which utilize a higher degree of reconstruction polynomial. Thus, in comparison with the previous work, the proposed PnTm−BVD−AD schemes have the benefit of a more compact stencil and lower cost. In summary, this work provides an alternative scheme for solving multi-scale problems in high speed compressible flows.

A new 3D OpenFoam solver with improved resolution for hyperbolic systems on hybrid unstructured grids

Although the accuracy and the robustness of discretized schemes solving hyperbolic systems have been greatly improved over the last two decades, devising a low-dissipative and non-oscillatory method remains a challenge. Especially, it is algorithmically complicated and computationally expensive to extend and apply high-resolution non-oscillatory schemes to 3D hybrid unstructured grids. Therefore, in this work we develop accurate, practical, and robust 3D hybrid unstructured OpenFoam solvers which can be applied in wide industrial applications. Different from existing 3D high order numerical solvers of which reconstruction schemes are based on polynomials of high degree, the proposed 3D scheme employs a polynomial function and a hyperbolic tangent basis function as two candidates for reconstruction functions. The MUSCL (Monotone Upstream-centered Schemes for Conservation law) scheme with the MLP (Multi-dimensional Limiting Process) slope limiter is adopted as the polynomial function. The multi-dimensional THINC (Tangent of Hyperbola for INterface Capturing) function with quadratic surface representation and Gaussian quadrature, so-called THINC/QQ, is used as the non-polynomial reconstruction candidate. With these reconstruction candidates, a multi-stage boundary variation diminishing (BVD) algorithm which significantly minimizes numerical dissipation is designed on 3D unstructured grids to select the final reconstruction function. With this accurate and robust reconstruction scheme, then we developed new solvers for simulating inviscid high speed compressible single-phase flow and two-phase flow via the implementation of the proposed scheme and algorithm into the open-source computational fluid dynamics (CFD) software, OpenFOAM. The solver with the proposed low-dissipative scheme, named as EulerEquationFoam-M-TQ-BVD, is constructed with the density-based solver for inviscid high speed compressible flow simulations. To simulate compressible multi-material flow with moving material interfaces, a solver named as FiveEquationFoam-M-TQ-BVD is developed based on mechanical-equilibrium diffusive interface model and MieGrüneisen equation of state. The performance of new solvers is evaluated through wide range benchmark tests and are compared with existing high order schemes such as the third-order WENO (Weighted Essentially Non-Oscillatory) scheme. The new solvers produce superior solution across critical points, contact discontinuities and material interfaces. Moreover, in comparison with WENO schemes, the proposed solver enjoys algorithmic simplicity and greater flexibility in 3D hybrid unstructured grids. Thus, this work provides accurate, practical and robust numerical solvers for high speed compressible single- and multi-material flow simulations.

IMMERSED BOUNDARY METHODS FOR THERMOFLUIDS PROBLEMS

We review the progress in the development and application of immersed boundary (IB) methods to thermofluids problems achieved in the last three decades. The implementation of different heat transfer boundary conditions, ranging from Dirichlet, Neumann, and Robin to conjugate heat transfer, are discussed for continuous as well as discrete forcing immersed boundary methods. We review several key studies that developed and employed IB methods with stationary boundaries for a variety of heat transfer scenarios such as forced convection, natural or mixed convection, radiation, and combustion. The computational challenges associated with the approaches employed for thermofluids problems with moving boundaries are discussed in detail. These include problems with rigid bodies that move under the influence of fluid dynamic forces as well as flow-induced deformation of compliant bodies. We conclude the article by briefly discussing the implementation of immersed boundary methods in two emerging areas: bioheat transfer and high-speed compressible flows.