A novel fluid–wall heat transfer model for molecular dynamics simulations

The ‘fluid–wall thermal equilibrium model’, to numerically simulate heating/cooling of fluid atoms by wall atoms, is used to compare molecular dynamics simulation results to the analytical solution of 1-D heat equation. Liquid argon atoms are placed between two platinum walls and simultaneous heating and cooling is simulated at the walls. Temperature gradient in liquid argon is evaluated and the results are found to match well with the analytical solution showing the physical soundness of the proposed model. Additional simulations are done where liquid argon atoms are heated by both the walls for two different channel heights and it is shown that in such cases, heat transfer occurs at a faster rate than predicted by heat equation with decreasing channel heights.     

A simplified CFD model for spectral radiative heat transfer in high-pressure hydrocarbon–air combustion systems

Detailed radiation modeling in piston engines has received relatively little attention to date. Recently, it is being revisited in light of current trends towards higher operating pressures and higher levels of exhaust-gas recirculation (EGR), both of which enhance molecular gas radiation. Advanced high-efficiency engines also are expected to function closer to the limits of stable operation, where even small perturbations to the energy balance can have a large influence on system behavior. Detailed radiation modeling using sophisticated tools like photon Monte Carlo/line-by-line (PMC/LBL) is computationally expensive. Here, guided by results from PMC/LBL, a simplified stepwise-gray spectral model in combination with a first-order spherical harmonics (P1 method) radiative transfer equation (RTE) solver is proposed and tested for engine-relevant conditions. Radiative emission, reabsorption and radiation reaching the walls are computed for a heavy-duty compression-ignition engine at part-load and full-load operating conditions with different levels of EGR and soot. The results are compared with those from PMC/LBL, P1/FSK (P1 with a full-spectrum k-distribution spectral model) and P1/Gray radiation models to assess the proposed model’s accuracy and computational cost. The results show that the proposed P1/StepwiseGray model can calculate reabsorption locally and globally with less than 10% error (with respect to PMC/LBL) at a small fraction of the computational cost of PMC/LBL (a factor of 30) and P1/FSK (a factor of 15). In contrast, error in computed reabsorption by the P1/Gray model is as high as 60%. It is expected that the simplified model should be broadly applicable to high-pressure hydrocarbon–air combustion systems, with or without soot.     

Coupled fluid–structure solver: The case of shock wave impact on monolithic and composite material plates

An unstructured adaptive mesh flow solver, a finite element structure solver and a moving mesh algorithm were implemented in the numerical simulation of the interaction between a shock wave and a structure. In the past, this interaction is mostly considered as one-way in the sense that the shock causes a transient load on the structure while it is reflected uneffected by the impact. A fully coupled approach was implemented in the present work which can account for the effects associated with a mutual interaction. This approach included a compressible flow Eulerian solver of second order accuracy in finite volume formulation for the fluid and a Langargian solver in finite element formulation for the solid structure. A novel implementation of advancing front moving mesh algorithm was made possible with the introduction of a flexible and efficient quad-edge data structure. Adaptive mesh refinement was introduced into the flow solver for improved accuracy as well. Numerical results are further validated by theoretical analysis, experimental data and results from other numerical simulations. Grid dependency study was performed and results showed that the physical phenomena and quantities were independent of the numerical grid chosen in the simulations. The results illuminated complicated flow phenomena and structure vibration patterns, which in order to be detected experimentally require capabilities beyond those of the current experimental techniques. The numerical simulations also successfully modelled the aero-acoustic damping effects on the structure, which do not exist in previous numerical models. Further analysis of the results showed that the mutual interaction is not linear and that the non-linearity arises because the wave propagation in the fluid is not linear and it cascades a non-linear and non-uniform loading on the plate. Non-linearity intensifies when the plate is vibrating at high frequency while the wave propagation speed is low.     

Stable loosely-coupled-type algorithm for fluid–structure interaction in blood flow

We introduce a novel loosely coupled-type algorithm for fluid–structure interaction between blood flow and thin vascular walls. This algorithm successfully deals with the difficulties associated with the “added mass effect”, which is known to be the cause of numerical instabilities in fluid–structure interaction problems involving fluid and structure of comparable densities. Our algorithm is based on a time-discretization via operator splitting which is applied, in a novel way, to separate the fluid sub-problem from the structure elastodynamics sub-problem. In contrast with traditional loosely-coupled schemes, no iterations are necessary between the fluid and structure sub-problems; this is due to the fact that our novel splitting strategy uses the “added mass effect” to stabilize rather than to destabilize the numerical algorithm. This stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub-problem. The stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable. Due to the crucial role played by the kinematic lateral boundary condition, the proposed algorithm is named the “kinematically coupled scheme”.     

A systematic approach for constructing higher-order immersed boundary and ghost fluid methods for fluid–structure interaction problems

A systematic approach is presented for constructing higher-order immersed boundary and ghost fluid methods for CFD in general, and fluid–structure interaction problems in particular. Such methods are gaining popularity because they simplify a number of computational issues. These range from gridding the fluid domain, to designing and implementing Eulerian-based algorithms for challenging fluid–structure applications characterized by large structural motions and deformations or topological changes. However, because they typically operate on non body-fitted grids, immersed boundary and ghost fluid methods also complicate other issues such as the treatment of wall boundary conditions in general, and fluid–structure transmission conditions in particular. These methods also tend to be at best first-order space-accurate at the immersed interfaces. In some cases, they are also provably inconsistent at these locations. A methodology is presented in this paper for addressing this issue. It is developed for inviscid flows and prescribed structural motions. For the sake of clarity, but without any loss of generality, this methodology is described in one and two dimensions. However, its extensions to flow-induced structural motions and three dimensions are straightforward. The proposed methodology leads to a departure from the current practice of populating ghost fluid values independently from the chosen spatial discretization scheme. Instead, it accounts for the pattern and properties of a preferred higher-order discretization scheme, and attributes ghost values as to preserve the formal order of spatial accuracy of this scheme. It is illustrated in this paper by its application to various finite difference and finite volume methods. Its impact is also demonstrated by one- and two-dimensional numerical experiments that confirm its theoretically proven ability to preserve higher-order spatial accuracy, including in the vicinity of the immersed interfaces.     

Analytical estimates of permeability and possible convective heat transfer in compact porous fluid–saturated rocks

The possible occurrence of convection in fine-grained (low-porous <15%) fluid-saturated (argon, water) rocks under hydrostatic pressures of up to 100 MPa is studied. Calculations of the Rayleigh filtration number and the Darcy number are presented. It is shown that the convective motion of fluid does not occur in pore-saturating fluids within the considered range of pressure variation, pore sizes, and temperature differences.     

A novel pressure–velocity formulation and solution method for fluid–structure interaction problems

In the standard approach for simulating fluid–structure interaction problems the solution of the set of equations for solids provides the three displacement components while the solution of equations for fluids provides the three velocity components and pressure. In the present paper a novel reformulation of the elastodynamic equations for Hookean solids is proposed so that they contain the same unknowns as the Navier–Stokes equations, namely velocities and pressure. A separate equation for pressure correction is derived from the constitutive equation of the solid material. The system of equations for both media is discretised using the same method (finite volume on collocated grids) and the same iterative technique (SIMPLE algorithm) is employed for the pressure–velocity coupling. With this approach, the continuity of the velocity field at the interface is automatically satisfied. A special pressure correction procedure that enforces the compatibility of stresses at the interface is also developed. The new method is employed for the prediction of pressure wave propagation in an elastic tube. Computations were carried out with different meshes and time steps and compared with available analytic solutions as well as with numerical results obtained using the Flügge equations that describe the deformation of thin shells. For all cases examined the method showed very good performance.     

A full Eulerian finite difference approach for solving fluid–structure coupling problems

A new simulation method for solving fluid–structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation [Hirt, Nichols, J. Comput. Phys. 39 (1981) 201], which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney–Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid–structure coupling problems is examined.     

A central Rankine–Hugoniot solver for hyperbolic conservation laws

A numerical method in which the Rankine–Hugoniot condition is enforced at the discrete level is developed. The simple format of central discretization in a finite volume method is used together with the jump condition to develop a simple and yet accurate numerical method free of Riemann solvers and complicated flux splittings. The steady discontinuities are captured accurately by this numerical method. The basic idea is to fix the coefficient of numerical dissipation based on the Rankine–Hugoniot (jump) condition. Several numerical examples for scalar and vector hyperbolic conservation laws representing the inviscid Burgers equation, the Euler equations of gas dynamics, shallow water equations and ideal MHD equations in one and two dimensions are presented which demonstrate the efficiency and accuracy of this numerical method in capturing the flow features.     

A matrix-free,implicit, incompressible fractional-step algorithm for fluid–structure interaction applications

In this paper we detail a fast, fully-coupled, partitioned fluid–structure interaction (FSI) scheme. For the incompressible fluid, new fractional-step algorithms are proposed which make possible the fully implicit, but matrix-free, parallel solution of the entire coupled fluid–solid system. These algorithms include artificial compressibility pressure-poisson solution in conjunction with upwind velocity stabilisation, as well as simplified pressure stabilisation for improved computational efficiency. A dual-timestepping approach is proposed where a Jacobi method is employed for the momentum equations while the pressures are concurrently solved via a matrix-free preconditioned GMRES methodology. This enables efficient sub-iteration level coupling between the fluid and solid domains. Parallelisation is effected for distributed-memory systems. The accuracy and efficiency of the developed technology is evaluated by application to benchmark problems from the literature. The new schemes are shown to be efficient and robust, with the developed preconditioned GMRES solver furnishing speed-ups ranging between 50 and 80.     

A direct-forcing embedded-boundary method with adaptive mesh refinement for fluid–structure interaction problems

In the present work we developed a structured adaptive mesh refinement (S-AMR) strategy for fluid–structure interaction problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different refinement levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. The grid topology and data-structure is managed using the Paramesh toolkit. The filtered Navier–Stokes equations for incompressible flow are advanced in time using an explicit second-order projection scheme, where all spatial derivatives are approximated using second-order central differences on a staggered grid. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used, where special attention is paid on the discontinuities introduced by the local refinement. For all the fluid–structure interaction problems reported in this study the complete set of equations governing the dynamics of the flow and the structure are simultaneously advanced in time using a predictor–corrector strategy. An embedded-boundary method is utilized to enforce the boundary conditions on a complex moving body which is not aligned with the grid lines. Several examples of increasing complexity are given to demonstrate the robustness and accuracy of the proposed formulation.     

A fixed-mesh method for incompressible flow–structure systems with finite solid deformations

A fixed-mesh algorithm is proposed for simulating flow–structure interactions such as those occurring in biological systems, in which both the fluid and solid are incompressible and the solid deformations are large. Several of the well-known difficulties in simulating such flow–structure interactions are avoided by formulating a single set of equations of motion on a fixed Eulerian mesh. The solid’s deformation is tracked to compute elastic stresses by an overlapping Lagrangian mesh. In this way, the flow–structure interaction is formulated as a distributed body force and singular surface force acting on an otherwise purely fluid system. These forces, which depend on the solid elastic stress distribution, are computed on the Lagrangian mesh by a standard finite-element method and then transferred to the fixed Eulerian mesh, where the joint momentum and continuity equations are solved by a finite-difference method. The constitutive model for the solid can be quite general. For the force transfer, standard immersed-boundary and immersed-interface methods can be used and are demonstrated. We have also developed and demonstrated a new projection method that unifies the transfer of the surface and body forces in a way that exactly conserves momentum; the interface is still effectively sharp for this approach. The spatial convergence of the method is observed to be between first- and second-order, as in most immersed-boundary methods for membrane flows. The algorithm is demonstrated by the simulations of an advected elastic disk, a flexible leaflet in an oscillating flow, and a model of a swimming jellyfish.     

A simple and efficient direct forcing immersed boundary framework for fluid–structure interactions

A direct forcing immersed boundary framework is presented for the simple and efficient simulation of strongly coupled fluid–structure interactions. The immersed boundary method developed by Yang and Balaras [J. Yang, E. Balaras, An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries, J. Comput. Phys. 215 (1) (2006) 12–40] is greatly simplified by eliminating several complicated geometric procedures without sacrificing the overall accuracy. The fluid–structure coupling scheme of Yang et al. [J. Yang, S. Preidikman, E. Balaras, A strongly-coupled, embedded-boundary method for fluid–structure interactions of elastically mounted rigid bodies, J. Fluids Struct. 24 (2008) 167–182] is also significantly expedited by moving the fluid solver out of the predictor–corrector iterative loop without altering the strong coupling property. Central to these improvements are the reformulation of the field extension strategy and the evaluation of fluid force and moment exerted on the immersed bodies, by taking advantage of the direct forcing idea in a fractional-step method. Several cases with prescribed motions are examined first to validate the simplified field extension approach. Then, a variety of strongly coupled fluid–structure interaction problems, including vortex-induced vibrations of a circular cylinder, transverse and rotational galloping of rectangular bodies, and fluttering and tumbling of rectangular plates, are computed. The excellent agreement between the present results and the reference data from experiments and other simulations demonstrates the accuracy, simplicity, and efficiency of the new method and its applicability in a wide range of complicated fluid–structure interaction problems.     

Nonlinear Rayleigh–Taylor instability of the cylindrical fluid flow with mass and heat transfer

The nonlinear Rayleigh–Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg–Landau equation. The F-expansion method is used to get exact solutions for a nonlinear Ginzburg–Landau equation. The region of solutions is displayed graphically.     

Energy transfer in hybrid systems quantum dot–plasmonic nanostructures

Radiationless relaxation in hybrid systems quantum dot (QD)–plasmonic nanostructure is considered. For the system QD–2D plasma the relaxation rate extremely steeply depends on the radius of quantum dot while in the pair QD–cylindrical wire contacting each other this dependence is logarithmic weak.     

A Langevin approach to the Log–Gauss–Pareto composite statistical structure

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.