Zhen-Hua Jiang, Xi Deng, Feng Xiao, Chao Yan, Jian Yu. A Higher Order Interpolation Scheme of Finite Volume Method for Compressible Flow on Curvilinear Grids. Communications in Computational Physics, 2020, 28 (4), pp.1609-1638. ⟨10.4208/cicp.OA-2019-0091⟩. ⟨hal-02960145⟩ Plus de détails...
A higher order interpolation scheme based on a multi-stage BVD (Boundary Variation Diminishing) algorithm is developed for the FV (Finite Volume) method on non-uniform, curvilinear structured grids to simulate the compressible turbulent flows. The designed scheme utilizes two types of candidate interpolants including a higher order linear-weight polynomial as high as eleven and a THING (Tangent of Hyperbola for INterface Capturing) function with the adaptive steepness. We investigate not only the accuracy but also the efficiency of the methodology through the cost efficiency analysis in comparison with well-designed mapped WENO (Weighted Essentially Non-Oscillatory) scheme. Numerical experimentation including benchmark broadband turbulence problem as well as real-life wall-bounded turbulent flows has been carried out to demonstrate the potential implementation of the present higher order interpolation scheme especially in the ILES (Implicit Large Eddy Simulation) of compressible turbulence.
Zhen-Hua Jiang, Xi Deng, Feng Xiao, Chao Yan, Jian Yu. A Higher Order Interpolation Scheme of Finite Volume Method for Compressible Flow on Curvilinear Grids. Communications in Computational Physics, 2020, 28 (4), pp.1609-1638. ⟨10.4208/cicp.OA-2019-0091⟩. ⟨hal-02960145⟩
Siengdy Tann, Xi Deng, Yuya Shimizu, Raphaël Loubère, Feng Xiao. Solution property preserving reconstruction for finite volume scheme: a boundary variation diminishing+multidimensional optimal order detection framework. International Journal for Numerical Methods in Fluids, 2020, 92 (6), pp.603-634. ⟨10.1002/fld.4798⟩. ⟨hal-02618891⟩ Plus de détails...
Xi Deng, Pierre Boivin. Diffuse interface modelling of reactive multi-phase flows applied to a sub-critical cryogenic jet. Applied Mathematical Modelling, 2020, ⟨10.1016/j.apm.2020.04.011⟩. ⟨hal-02561937⟩ Plus de détails...
In order to simulate cryogenic H 2 − O 2 jets under subcritical condition, a numerical model is constructed to solve compressible reactive multi-component flows which involve complex multi-physics processes such as moving material interfaces, shock waves, phase transition and combustion. The liquid and reactive gaseous mixture are described by a homogeneous mixture model with diffusion transport for heat, momentum and species. A hybrid thermodynamic closure strategy is proposed to construct an equation of state (EOS) for the mixture. The phase transition process is modeled by a recent fast relaxation method which gradually reaches the thermo-chemical equilibrium without iterative process. A simplified transport model is also implemented to ensure the accurate behavior in the limit of pure fluids and maintain computational efficiency. Last, a 12-step chemistry model is included to account for hydrogen combustion. Then the developed numerical model is solved with the finite volume method where a low dissipation AUSM (advection upstream splitting method) Riemann solver is extended for multi-component flows. A homogeneous reconstruction strategy compatible with the homogeneous mixture model is adopted to prevent numerical oscillations across material interfaces. Having included these elements, the model is validated on a number of canonical configurations, first for multi-phase flows, and second for reactive flows. These tests allow recovery of the expected behavior in both the multiphase and reactive limits, and the model capability is further demonstrated on a 2D burning cryogenic H 2 − O 2 jet, in a configuration reminiscent of rocket engine ignition.
Xi Deng, Pierre Boivin. Diffuse interface modelling of reactive multi-phase flows applied to a sub-critical cryogenic jet. Applied Mathematical Modelling, 2020, ⟨10.1016/j.apm.2020.04.011⟩. ⟨hal-02561937⟩
Xi Deng, Yuya Shimizu, Bin Xie, Feng Xiao. Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm. Computers and Fluids, Elsevier, 2020, 200, pp.104433. ⟨10.1016/j.compfluid.2020.104433⟩. ⟨hal-02892513⟩ Plus de détails...
Based on the fifth-order scheme in our previous work (Deng et. al (2019) [28]), a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called PnTm - BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm), are designed by employing high-order upwind-biased interpolations and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminishing) algorithm so as to effectively control numerical oscillation and dissipation. We devise the new schemes up to eleventh order in an efficient way by directly increasing the order of the underlying upwind scheme using high order polynomials. The analysis of the spectral property and accuracy tests show that the new reconstruction strategy well preserves the low-dissipation property of the underlying upwind schemes with high-order polynomials for smooth solution over all wave numbers and realizes n + 1 order convergence rate. The performance of new schemes is examined through widely used benchmark tests, which demonstrate that the proposed schemes are capable of simultaneously resolving small-scale flow features with high resolution and capturing discontinuities with low dissipation. With outperforming results and simplicity in algorithm, the new reconstruction strategy shows great potential as an alternative numerical framework for computing nonlinear hyperbolic conservation laws that have discontinuous and smooth solutions of different scales.
Xi Deng, Yuya Shimizu, Bin Xie, Feng Xiao. Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm. Computers and Fluids, Elsevier, 2020, 200, pp.104433. ⟨10.1016/j.compfluid.2020.104433⟩. ⟨hal-02892513⟩
Xi Deng, Yuya Shimizu, Bin Xie, Feng Xiao. Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm. Computers and Fluids, 2020, 200, pp.104433. ⟨10.1016/j.compfluid.2020.104433⟩. ⟨hal-02892513⟩ Plus de détails...
Based on the fifth-order scheme in our previous work (Deng et. al (2019) [28]), a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called PnTm - BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm), are designed by employing high-order upwind-biased interpolations and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminishing) algorithm so as to effectively control numerical oscillation and dissipation. We devise the new schemes up to eleventh order in an efficient way by directly increasing the order of the underlying upwind scheme using high order polynomials. The analysis of the spectral property and accuracy tests show that the new reconstruction strategy well preserves the low-dissipation property of the underlying upwind schemes with high-order polynomials for smooth solution over all wave numbers and realizes n + 1 order convergence rate. The performance of new schemes is examined through widely used benchmark tests, which demonstrate that the proposed schemes are capable of simultaneously resolving small-scale flow features with high resolution and capturing discontinuities with low dissipation. With outperforming results and simplicity in algorithm, the new reconstruction strategy shows great potential as an alternative numerical framework for computing nonlinear hyperbolic conservation laws that have discontinuous and smooth solutions of different scales.
Xi Deng, Yuya Shimizu, Bin Xie, Feng Xiao. Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm. Computers and Fluids, 2020, 200, pp.104433. ⟨10.1016/j.compfluid.2020.104433⟩. ⟨hal-02892513⟩
Implicit large eddy simulation (ILES) of compressible turbulence with shock capturing schemes requires wide investigations and numerical experiments. In this study, a newly proposed PnTm - BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm) shock capturing scheme is introduced to simulate compressible turbulence flow with ILES. The new scheme is designed by employing high-order linear-weight polynomials and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminishing) algorithm so as to effectively control numerical oscillation and dissipation. Numerical tests involving shock waves and broadband turbulence are conducted in comparison with WENO (Weighted Essentially Non-oscillatory) schemes which are widely used in ILES. The results demonstrate performing ILES with PnTm- BVD scheme is able to obtain higher resolution and more faithful results than WENO does. Importantly, the superiority of PnTm-BVD becomes more notable in high wave-number region. Thus this paper provides and verifies a new scheme which is promising in providing high-resolution results for real-case ILES of compressible turbulence flow.
Xi Deng, Zhen-Hua Jiang, Feng Xiao, Chao Yan. Implicit large eddy simulation of compressible turbulence flow with PnTm − BVD scheme. Applied Mathematical Modelling, 2020, 77, pp.17-31. ⟨10.1016/j.apm.2019.07.022⟩. ⟨hal-03235122⟩
Implicit large eddy simulation (ILES) of compressible turbulence with shock capturing schemes requires wide investigations and numerical experiments. In this study, a newly proposed PnTm - BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm) shock capturing scheme is introduced to simulate compressible turbulence flow with ILES. The new scheme is designed by employing high-order linear-weight polynomials and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminishing) algorithm so as to effectively control numerical oscillation and dissipation. Numerical tests involving shock waves and broadband turbulence are conducted in comparison with WENO (Weighted Essentially Non-oscillatory) schemes which are widely used in ILES. The results demonstrate performing ILES with PnTm- BVD scheme is able to obtain higher resolution and more faithful results than WENO does. Importantly, the superiority of PnTm-BVD becomes more notable in high wave-number region. Thus this paper provides and verifies a new scheme which is promising in providing high-resolution results for real-case ILES of compressible turbulence flow.
Xi Deng, Zhen-Hua Jiang, Feng Xiao, Chao Yan. Implicit large eddy simulation of compressible turbulence flow with PnTm − BVD scheme. Applied Mathematical Modelling, 2020, 77, pp.17-31. ⟨10.1016/j.apm.2019.07.022⟩. ⟨hal-02892550⟩
Bin Xie, Xi Deng, Shijun Liao. High-fidelity solver on polyhedral unstructured grids for low-Mach number compressible viscous flow. Computer Methods in Applied Mechanics and Engineering, 2019, 357, pp.112584. ⟨10.1016/j.cma.2019.112584⟩. ⟨hal-02467981⟩ Plus de détails...
In this article, we developed an unstructured fluid solver based on finite volume framework for the low-Mach number compressible flows. The present method, so-called FVMS3 (Finite Volume method based on Merged Stencil with 3rd-order reconstruction) formulates two different numerical procedures for spatial reconstructions based on the quadratic polynomial which is performed by using least-square approximations on a merged stencil. In order to improve the reconstruction for discontinuities, we propose the limiting projection approach and smoothness adaptive fitting (SAF) scheme to suppress the numerical oscillation and limit the numerical dissipation. The resulting discretization algorithm that combines FVMS3 with SAF-based limiting projection scheme has third-order accuracy and resolves both smooth and non-smooth solutions with excellent quality. Additionally, a novel numerical model has been proposed by introducing the advection upstream splitting method (AUSM) flux into the pressure projection formulation which results in a unified scheme that works uniformly up to the incompressible limit. The fluid solver that integrates all above new efforts provides high-fidelity solutions for compressible viscous flows particularly for the low Mach regime. The performance of this new solver is verified by numerous benchmark tests. Our numerical results show that the proposed scheme gives accurate and robust solutions for a wide spectrum of test problems.
Bin Xie, Xi Deng, Shijun Liao. High-fidelity solver on polyhedral unstructured grids for low-Mach number compressible viscous flow. Computer Methods in Applied Mechanics and Engineering, 2019, 357, pp.112584. ⟨10.1016/j.cma.2019.112584⟩. ⟨hal-02467981⟩
Journal: Computer Methods in Applied Mechanics and Engineering
Siengdy Tann, Xi Deng, Yuya Shimizu, Raphaël Loubère, Feng Xiao. Solution Property Preserving Reconstruction for Finite Volume Scheme: a BVD+MOOD framework. International Journal for Numerical Methods in Fluids, In press, ⟨10.1002/fld.4798⟩. ⟨hal-02397156⟩ Plus de détails...
The purpose of this work is to build a general framework to reconstruct the underlying fields within a Finite Volume (FV) scheme solving a hyperbolic system of PDEs (Partial Differential Equations). In an FV context, the data are piece-wise constants per computational cell and the physical fields are reconstructed taking into account neighbor cell values. These reconstructions are further used to evaluate the physical states usually used to feed a Riemann solver which computes the associated numerical fluxes. The physical field reconstructions must obey some properties linked to the system of PDEs such as the positivity, but also some numerically based ones, like an essentially non-oscillatory behaviour. Moreover, the reconstructions should be high accurate for smooth flows and robust/stable for discontinuous solutions. To ensure a Solution Property Preserving Reconstruction, we introduce a methodology to blend high/low order polynomials and hyperbolic tangent reconstructions. A Boundary Variation Diminishing (BVD) algorithm is employed to select the best reconstruction in each cell. An a posteriori MOOD detection procedure is employed to ensure the positivity by re-computing the rare problematic cells using a robust first-order FV scheme. We illustrate the performance of the proposed scheme via the numerical simulations for some benchmark tests which involve vacuum or near vacuum states, strong discontinuities and also smooth flows. The proposed scheme maintains high accuracy on smooth profile, preserves the positivity and can eliminate the oscillations in the vicinity of discontinuities while maintaining sharper discontinuity with superior solution quality compared to classical high accurate FV schemes.
Siengdy Tann, Xi Deng, Yuya Shimizu, Raphaël Loubère, Feng Xiao. Solution Property Preserving Reconstruction for Finite Volume Scheme: a BVD+MOOD framework. International Journal for Numerical Methods in Fluids, In press, ⟨10.1002/fld.4798⟩. ⟨hal-02397156⟩
Journal: International Journal for Numerical Methods in Fluids
Xi Deng, Pierre Boivin, Feng Xiao. A new formulation for two-wave Riemann solver accurate at contact interfaces. Physics of Fluids, 2019, 31 (4), pp.046102. ⟨10.1063/1.5083888⟩. ⟨hal-02100764⟩ Plus de détails...
This study proposes a new formulation for Harten, Lax and van Leer (HLL) type Riemann solver which is capable of solving contact discontinuities accurately but with robustness for strong shock. It is well known that the original HLL, which has incomplete wave structures, is too dissipative to capture contact disconti-nuities accurately. On the other side, contact-capturing approximate Riemann solvers such as Harten, Lax and van Leer with Contact (HLLC) usually suffer from spurious solutions, also called carbuncle phenomenon, for strong shock. In this work a new accurate and robust HLL-type formulation, so-called HLL-BVD (HLL Riemann solver with BVD) is proposed by modifying the original HLL with BVD (boundary variation dimin-shing) algorithm. Instead of explicitly recovering the complete wave structures like the way of HLLC, the proposed method restores the missing contact with a jump-like function. The capability of solving contact discontinuities is further improved by minimizing the inherent dissipation term in HLL. Without modifying the original incomplete wave structures of HLL, the robustness for strong shock has been reserved. Thus the proposed method is free from shock instability problem. The accuracy and robustness of the new method are demonstrated through solving several one-and two-dimensional tests. Results indicate that the new formulation based on two-wave HLL-type Riemann solver is not only capable of capturing contact waves more accurately than the original HLL or HLLC but, most importantly, is free form carbuncle instability for strong shock.
Xi Deng, Pierre Boivin, Feng Xiao. A new formulation for two-wave Riemann solver accurate at contact interfaces. Physics of Fluids, 2019, 31 (4), pp.046102. ⟨10.1063/1.5083888⟩. ⟨hal-02100764⟩
Xi Deng, Bin Xie, R. Loubère, Yuya Shimizu, Feng Xiao. Limiter-free discontinuity-capturing scheme for compressible gas dynamics with
reactive fronts. Computers and Fluids, Elsevier, In press, 171, pp.1-14. ⟨10.1016/j.compfluid.2018.05.015⟩. ⟨hal-01791898⟩ Plus de détails...
This work proposes a new spatial reconstruction scheme in finite volume frameworks. Different from long-lasting reconstruction processes which employ high order polynomials enforced with some carefully designed limiting pro- jections to seek stable solutions around discontinuities, the current discretized scheme employs THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive sharpness to solve both smooth and discontinuous solutions. Due to the essentially monotone and bounded properties of THINC function, difficulties to solve sharp discontinuous solutions and complexities associated with designing limiting projections can be prevented. A new simplified BVD (Boundary Variations Diminishing) algorithm, so-called adaptive THINC-BVD, is devised to reduce numerical dissipations through minimizing the total boundary variations for each cell. Verified through numerical tests, the present method is able to capture both smooth and discontinuous solutions in Euler equations for com- pressible gas dynamics with excellent solution quality competitive to other existing schemes. More profoundly, it provides an accurate and reliable solver for a class of reactive compressible gas flows with stiff source terms, such as the gaseous detonation waves, which are quite challenging to other high-resolution schemes. The stiff C-J detonation benchmark test reveals that the adaptive THINC-BVD scheme can accurately capture the reacting front of the gaseous detonation, while the WENO scheme with the same grid resolution generates unacceptable results. Owing also to its algorithmic simplicity, the proposed method can become as a practical and promising numerical solver for compress- ible gas dynamics, particularly for simulations involving strong discontinuities and reacting fronts with stiff source term.
Xi Deng, Bin Xie, R. Loubère, Yuya Shimizu, Feng Xiao. Limiter-free discontinuity-capturing scheme for compressible gas dynamics with
reactive fronts. Computers and Fluids, Elsevier, In press, 171, pp.1-14. ⟨10.1016/j.compfluid.2018.05.015⟩. ⟨hal-01791898⟩
