International Jrnl For Numerical Methods in Fluids

doi: 10.1002/fld.5006pmid: N/A

Lyras, Konstantinos G.; Lee, Jack

doi: 10.1002/fld.5082pmid: N/A

This article presents a finite volume method for simulating two‐phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that the interface is calculated in order to satisfy mass conservation with no explicit interface reconstruction step and the mass fluxes across cell‐faces are corrected to respect the recovered volume fraction. The mass‐conservation correction step proposed here, is utilized using an iterative algorithm which solves a reaction‐diffusion equation for the mass correction of the level set. The re‐sharpened volume fraction is used for the new volumetric fluxes at each cell which are calculated through the proposed algorithm that guarantees that they satisfy mass conservation. The algorithm is not limited in representing the interface with the 0.5‐contour and is applicable for arbitrary polyhedral cells. Good accuracy and mass conservation are achieved when compared to other conservative approaches.

Amaro Junior, Rubens Augusto; Gay Neto, Alfredo; Cheng, Liang‐Yee

doi: 10.1002/fld.5083pmid: N/A

A three‐dimensional fluid–structure interaction solver based on an improved weakly compressible moving particle simulation (WC‐MPS) method and a geometrically nonlinear shell structural model is developed and applied to hydro‐elastic free‐surface flows. The fluid–structure coupling is performed by a polygon wall boundary model that can handle particles and finite elements of distinct sizes. In WC‐MPS, a tuning‐free diffusive term is introduced to the continuity equation to mitigate nonphysical pressure oscillations. Discrete divergence operators are derived and applied to the polygon wall boundary, of which the numerical stability is enhanced by a repulsive Lennard–Jones force. Additionally, an efficient technique to deal with the interaction between fluid particles placed at opposite sides of zero‐thickness walls is proposed. The geometrically nonlinear shell is modeled by an unstructured mesh of six‐node triangular elements. Finite rotations are considered with Rodrigues parameters and a hyperelastic constitutive model is adopted. Benchmark examples involving free‐surface flows and thin‐walled structures demonstrate that the proposed model is robust, numerically stable and offers more efficient computation by allowing mesh size larger than that of fluid particles.

Christopher, Joshua; Guzik, Stephen M.; Gao, Xinfeng

doi: 10.1002/fld.5084pmid: N/A

The objective of this study is to develop and apply efficient solution techniques for numerical modeling of combustion with stiff chemical kinetics in practical combustors. The new technique combines a fourth‐order implicit‐explicit (IMEX) additive Runge‐Kutta scheme (ARK) with adaptive mesh refinement (AMR). The IMEX component treats the stiff reactions implicitly but integrates convection and diffusion explicitly in time, and thus permits the solution to advance with larger time‐step sizes than that of explicit time‐marching methods alone. The AMR further adds computational efficiency by effectively placing high spatial resolution meshes in regions with strong gradients, such as flame fronts. The novelty of this study is in the integration of a fourth‐order IMEX ARK method with AMR for a high‐order finite‐volume scheme and the application to solving complex reacting flows governed by the compressible Navier–Stokes equations with very stiff chemistry in a practical combustor geometry. The effectiveness and performance of the adaptive ARK4 is assessed for complex reacting flows by examining properties, such as the presence of shock waves, the time‐scale changes in response to AMR levels, and the size and stiffness of reaction mechanisms for various fuels such as H2$$ {\mathrm{H}}_2 $$, CH4$$ {\mathrm{CH}}_4 $$, and C3H8$$ {\mathrm{C}}_3{\mathrm{H}}_8 $$. The new adaptive ARK4 method is verified and validated using a convection‐diffusion‐reaction problem and shock‐driven combustion, respectively. The validated algorithm is then applied to solve the stiff C3H8$$ {\mathrm{C}}_3{\mathrm{H}}_8 $$‐air combustion in a bluff‐body combustor. A significant speedup of three orders of magnitude is achieved in comparison to the standard ERK4 method at the given solution accuracy.

Gehrke, Martin; Rung, Thomas

doi: 10.1002/fld.5085pmid: N/A

The article is concerned with the assessment of a cumulant lattice Boltzmann method in wall‐bounded, separated turbulent shear flows. The approach is of interest for its resolution‐spanning success in turbulent channel flows without using a specific turbulence treatment. The assessment focuses upon the flow over a periodic hill, which offers a rich basis of numerical and experimental data, for Reynolds numbers within 700≤Re≤37,000. The analysis involves the mean flow field, second moments and their invariants, as well as spectral data obtained for a wide range of resolutions with 2≲Δxi+≲100. With the emphasis on a recently published parameterized cumulant collision operator, the universality of the value assigned to a stability preserving regularization parameter is assessed. Reported results guide resolution‐dependent optimized values and indicate a required minimum resolution of Δxi+≈30. Analog to the findings for attached turbulent shear flows, the approach appears to adequately resolve complex turbulent flows without the need for ad hoc modeling for a range of scale resolving resolutions.

Batteux, Léa; Duval, Fabien; Herbin, Raphaële; Latché, Jean‐Claude; Poullet, Pascal

doi: 10.1002/fld.5086pmid: N/A

The purpose in this article is to design finite‐volume schemes on structured grids for the transport of piecewise‐constant functions (typically, indicator functions) with as low diffusion as possible. We first propose an extension of the so‐called Lagrange‐projection algorithm, or downwind scheme with an Ultrabee limiter, for the transport equation in one space dimension with a non‐constant velocity; as its constant velocity counterpart, this scheme is designed to capture the discontinuities separating two plateaus in only one cell, and is referred to as “anti‐diffusive.” It is shown to preserve the bounds of the solution. Then, for two and three dimensional problems, we introduce a conservative alternate‐directions algorithm, an show that this latter enjoys a discrete maximum principle, provided that the underlying one‐dimensional schemes satisfy a property which may be seen as a flux limitation, possibly incorporated a posteriori in any explicit scheme. Numerical tests of this alternate‐directions algorithm are performed, with a variety of one‐dimensional embedded schemes including the anti‐diffusive scheme developed here and the so called THINC scheme. The observed numerical diffusion is indeed very low. With the anti‐diffusive scheme, the above‐mentioned a posteriori limitation is necessary to preserve the solution bounds, but, in the performed tests, does not introduce any visible additional diffusion.

Re, Barbara; Abgrall, Rémi

doi: 10.1002/fld.5087pmid: N/A

Within the framework of diffuse interface methods, we derive a pressure‐based Baer–Nunziato type model well‐suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes relaxation terms characterized by user‐defined finite parameters, which drive the pressure and velocity of each phase toward the equilibrium. There is no clear notion of speed of sound, and thus, most of the classical low Mach approximation cannot easily be cast in this context. The proposed solution strategy consists of two operators: a semi‐implicit finite‐volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. Being the acoustic terms in the hyperbolic part integrated implicitly, the stability condition on the time step is lessened. The discretization of nonconservative terms involving the gradient of the volume fraction fulfills by construction the nondisturbance condition on pressure and velocity to avoid oscillations across the multimaterial interfaces. The developed simulation tool is validated through one‐dimensional simulations of shock‐tube and Riemann‐problems, involving water‐aluminum and water‐air mixtures, vapor‐liquid mixture of water and of carbon dioxide, and almost pure flows. The numerical results match analytical and reference ones, except some expected discrepancies across shocks, which however remain acceptable (errors within some percentage points). All tests were performed with acoustic CFL numbers greater than one, and no stability issues arose, even for CFL greater than 10. The effects of different values of relaxation parameters and of different amount equations of state—stiffened gas and Peng–Robinson—were investigated.

Yang, Di; Gao, Zhiming; Ni, Guoxi

doi: 10.1002/fld.5088pmid: N/A

Two kinds of nonlinear cell‐centered positivity‐preserving finite volume schemes are proposed for the anisotropic diffusion problems on general three‐dimensional polyhedral meshes. First, the one‐sided flux on the cell‐faces is discretized using the fixed stencil of all vertices, then the cell‐centered discretization scheme is obtained using the nonlinear two‐point flux approximation. On this basis, a new explicit weighted second‐order vertex interpolation algorithm for arbitrary polyhedral meshes is designed to eliminate the vertex auxiliary unknowns in the scheme. In addition, an improved Anderson acceleration algorithm is adopted for nonlinear iteration. Finally, some benchmark examples are given to verify the convergence and positivity‐preserving property of the two schemes.

Colombo, Alessandro; Crivellini, Andrea; Ghidoni, Antonio; Nigro, Alessandra; Noventa, Gianmaria

doi: 10.1002/fld.5089pmid: N/A

In the last decades flow simulations have become a routine practice in many industrial fields for the aerodynamic and noise prediction. Moreover, the ever increasing interest in simulating off‐design operating conditions promoted the development of high‐fidelity simulation tools to overcome the modeling and accuracy limits of standard industrial codes in predicting turbulent separated flows. The discontinuous Galerkin (DG) method is well suited for this class of simulations, but today DG‐based CFD and CAA (Computational AeroAcoustics) solvers cannot yet reach the computational efficiency of well‐established commercial codes. As a consequence, the present paper aims at exploiting some attractive strategies, such as the adaptation of the elemental polynomial degree (p‐adaptation) and of the degree of exactness of quadrature rules, to enhance the computational efficiency of an implicit DG platform for CFD and CAA simulations. Moreover, a sponge layer non‐reflecting boundary treatment has been also implemented for CAA. The predicting capabilities of the method have been assessed on classical CAA and CFD test cases. The proposed adaptive strategy guarantees a significant reduction ( ≈50%) of the computational effort for both CFD and CAA simulations, compared to uniform‐order discretizations, while not spoiling the high accuracy requested to an high‐fidelity simulation tool.

Pan, Wei; Kramer, Stephan C.; Piggott, Matthew D.; Yu, Xiping

doi: 10.1002/fld.5090pmid: N/A

A new two‐layer model for impulsive wave generation by deformable granular landslides is developed based upon a discontinuous Galerkin finite element discretization. Landslide motion is modeled using a depth‐averaged formulation for a shallow subaerial debris flow, which considers the bed curvature represented by the local slope angle variable and accounts for inter‐granular stresses using Coulomb friction. Wave generation and propagation are simulated with the three‐dimensional non‐hydrostatic coastal ocean model Thetis to accurately capture key features such as wave dispersion. Two different techniques are used in treating wetting and drying (WD) processes during the landslide displacement and wave generation, respectively. For the lower‐layer landslide motion across the dry bed a classical thin‐layer explicit WD method is implemented, while for the resulting free‐surface waves interacted with the moving landslide an implicit WD scheme is utilized to naturally circumvent the artificial pressure gradient problem which may appear in the dynamic interaction between the landslide and water if using the thin‐layer method. The two‐layer model is validated using a suite of test cases, with the resulting good agreement demonstrating its capability in describing both the complex behaviors of granular landslides from initiation to deposition, and the consequent wave generation and propagation.