Structure topology optimization: fully coupled level set method via FEMLAB

This paper presents a procedure which can easily implement the 2D compliance minimization structure topology optimization by the level set method using the FEMLAB package. Instead of a finite difference solver for the level set equation, as is usually the case, a finite element solver for the reaction–diffusion equation is used to evolve the material boundaries. All of the optimization procedures are implemented in a user-friendly manner. A FEMLAB code can be downloaded from the homepage www.imtek.de/simulation and is free for educational purposes.     

On enhanced non-linear free surface flow simulations with a hybrid LBM–VOF model

In this paper, we present extensions, extensive validations and applications of our previously published hybrid volume-of-fluid-based (VOF) model for the simulation of free-surface flow problems. For the solution of the flow field, the lattice Boltzmann method is used, where the free surface is represented by a VOF approach. The advection equation for the VOF fill level is discretized with a finite volume method, on the basis of a 3D Piecewise Linear Interface Reconstruction (PLIC) algorithm. The model is validated for several standard free surface benchmarks, such as breaking dam scenarios and a free falling jet. Finally, the hybrid algorithm is applied to the simulation of a wave breaking by overturning during shoaling, which is considered to be a demanding test case, especially for VOF solvers. In this case, the flow field is initialized early in the shoaling process with a solitary wave solution from inviscid, irrotational potential flow. The wave breaking process is then simulated with the 3D transient and turbulent LBM–VOF solver. All validation and benchmark tests confirm the accuracy of the proposed hybrid model.     

C3: A finite volume-finite difference hybrid model for tsunami propagation and runup

A numerical model that couples Finite Difference and Finite Volume schemes has been developed for tsunami propagation and runup study. An explicit leap-frog scheme and a first order upwind scheme has been considered in the Finite Difference module, while in the Finite Volume scheme a Godunov Type method based on the f-waves approach has been used. The Riemann solver included in the model corresponds to an approximate augmented solver for the Shallow Water Equations (SWE) in the presence of variable bottom surface. With this hybrid model some of the problems inherent to the Godunov type schemes are avoided in the offshore region, while in the coastal area the use of a conservative method ensures the correct computation of the runup and wave breaking. The model has been tested and validated using different problems with a known analytical solution and also with laboratory experiments, considering both non breaking and breaking waves. The results are very satisfactory, showing that the hybrid approach is a useful technique for practical usages.     

A <Emphasis Type="Italic">p</Emphasis>-Adaptive Local Discontinuous Galerkin Level Set Method for Willmore Flow

The level set method is often used to capture interface behavior in two or three dimensions. In this paper, we present a combination of a local discontinuous Galerkin (LDG) method and a level set method for simulating Willmore flow. The LDG scheme is energy stable and mass conservative, which are good properties compared with other numerical methods. In addition, to enhance the efficiency of the proposed LDG scheme and level set method, we employ a p-adaptive local discontinuous Galerkin technique, which applies high order polynomial approximations around the zero level set and low order ones away from the zero level set. A major advantage of the level set method is that the topological changes are well defined and easily performed. In particular, given the stiffness and high nonlinearity of Willmore flow, a high order semi-implicit Runge–Kutta method is employed for time discretization, which allows larger time steps. These equations at the implicit time level are linear, we demonstrate an efficient and practical multigrid solver to solve the equations. Numerical examples are given to illustrate that the combination of the LDG scheme and level set method provides an efficient and practical approach to simulate the Willmore flow.     

On the application of the single-phase level set method to naval hydrodynamic flows

The application of the single-phase level set approach to the numerical simulations of three-dimensional free surface flows around complex geometries, at both non-breaking and breaking regimes is presented. In this approach only the liquid phase is simulated and the level set function is used as tracking device to locate the free surface position. The extrapolation of the solution in the dummy points in the gaseous phase is such that second-order accuracy is maintained also in the points adjacent to the free surface; the time evolution of the level set function and the re-initialization step have been merged so to get a function which is a distance function everywhere, and satisfies, at the same time, the kinematic condition on the free surface. The implementation of this technique into a general purpose Reynolds averaged Navier-Stokes (RANS) equations solver developed at INSEAN [Di Mascio A, Broglia R, Favini B. A Second Order Godunov-type Scheme for Naval Hydrodynamics. Kluwer Academic/Plenum Publishers; 2001, p. 253-61], is described in details; capabilities of the algorithm in dealing with non-breaking and breaking flows in the naval hydrodynamic context will be demonstrated by using a submerged hydrofoil and two different ship hulls in straight course as test cases. Comparisons with both experimental data and numerical surface fitting computations are presented; convergence properties of the algorithm, as well as validation and verification assessment will be also discussed.     

Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow

We propose a method for the data‐driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flow problems, and we propose a novel LSTM‐based approach to predict the changes of the pressure field over time. The central challenge in this context is the high dimensionality of Eulerian space‐time data sets. We demonstrate for the first time that dense 3D+time functions of physics system can be predicted within the latent spaces of neural networks, and we arrive at a neural‐network based simulation algorithm with significant practical speed‐ups. We highlight the capabilities of our method with a series of complex liquid simulations, and with a set of single‐phase buoyancy simulations. With a set of trained networks, our method is more than two orders of magnitudes faster than a traditional pressure solver. Additionally, we present and discuss a series of detailed evaluations for the different components of our algorithm.     

Accelerated numerical simulations of a heaving floating body by coupling a motion solver with a two-phase fluid solver

This paper presents a study on the coupling between a fluid solver and a motion solver to perform fluid–structure interaction (FSI) simulations of floating bodies such as point absorber wave energy converters heaving under wave loading. The two-phase fluid solver with dynamic mesh handling, interDyMFoam, is a part of the Computational Fluid Dynamics (CFD) toolbox OpenFOAM. The incompressible Navier–Stokes (NS) equations are solved together with a conservation equation for the Volume of Fluid (VoF). The motion solver is computing the kinematic body motion induced by the fluid flow. A coupling algorithm is needed between the fluid solver and the motion solver to obtain a converged solution between the hydrodynamic flow field around and the kinematic motion of the body during each time step in the transient simulation. For body geometries with a significant added mass effect, simple coupling algorithms show slow convergence or even instabilities. In this paper, we identify the mechanism for the numerical instability and we derive an accelerated coupling algorithm (based on a Jacobian) to enhance the convergence speed between the fluid and motion solver. Secondly, we illustrate the coupling algorithm by presenting a free decay test of a heaving wave energy converter. Thirdly and most challenging, a water impact test of a free falling wedge with a significant added mass effect is successfully simulated. For both test cases, the numerical results obtained by using the accelerated coupling algorithm are in a very good agreement with the experimental measurements.     

Propagation of gravity waves through an SPH scheme with numerical diffusive terms

Basing on the work by Antuono et al. (2010) [1], an SPH model with numerical diffusive terms (here denoted δ-SPH) is combined with an enhanced treatment of solid boundaries to simulate 2D gravity waves generated by a wave maker and propagating into a basin. Both regular and transient wave systems are considered. In the former, a large number of simulations is performed for different wave steepness and height-to-depth ratio and the results are compared with a BEM Mixed-Eulerian–Lagrangian solver (here denoted BEM-MEL solver). In the latter, the δ-SPH model has been compared with both the experimental measurements available in the literature and with the BEM-MEL solver, at least until the breaking event occurs. The results show a satisfactory agreement between the δ-SPH model, the BEM-MEL solver and the experiments. Finally, the influence of the weakly-compressibility assumption on the SPH results is inspected and a convergence analysis is provided in order to identify the minimal spatial resolution needed to get an accurate representation of gravity waves.     

Numerical simulation of cavitating flows with homogeneous models

The simulation of cavitating flows is a challenging problem both in terms of modelling the physics and developing robust numerical methodologies. Such flows are characterized by important variations of the local Mach number and involve thermodynamic phase transition. To simulate these flows by applying homogeneous models, an appropriate equation of state (EOS) is necessary to cover all possible fluid states (pure liquid, two-phase mixture and pure vapour). Moreover, the numerical method has to handle any Mach number accurately. This paper presents a one-fluid compressible Reynolds-Averaged Navier–Stokes (RANS) solver with a preconditioning scheme. The cavitation phenomenon is modelled by two different liquid–vapour mixture EOS. The mathematical and thermodynamic properties are studied. Steady and unsteady numerical results are given for a Venturi geometry and comparisons are made with experimental data.     

Construction of modified embedded atom method potentials for the study of the bulk phase behaviour in binary Pt–Rh, Pt–Pd, Pd–Rh and ternary Pt–Pd–Rh alloys

A first attempt is made to simulate the solid part of the phase diagram of the ternary Pt–Pd–Rh system. To this end, Monte Carlo (MC) simulations are combined with the Modified Embedded Atom Method (MEAM) and optimised parameters entirely based on Density Functional Theory (DFT) data. This MEAM potential is first validated by calculating the heat of mixing or the demixing phase boundary for the binary subsystems Pt–Rh, Pt–Pd and Pd–Rh. For the disordered alloy systems Pt–Rh and Pt–Pd, the MC/MEAM simulation results show a slightly exothermic heat of mixing, thereby contradicting any demixing behaviour, in agreement with other theoretical results. For the Pd–Rh system the experimentally observed demixing region is very well reproduced by the MC/MEAM simulations. The extrapolation of the MEAM potentials to ternary systems is next validated by comparing DFT calculations for the energy of formation of ordered Pt–Pd–Rh compounds with the corresponding MEAM energies. Finally, the validated potential is used for the calculation of the ternary phase diagram at 600 K.     

Explicit Hybrid Time Domain Solver for the Maxwell Equations in 3D

We present an accurate and efficient explicit hybrid solver for Maxwell's equations in time domain. The hybrid solver combines FD-TD with an unstructured finite volume solver. The finite volume solver is a generalization of FD-TD to unstructured grids and it uses a third-order staggered Adams–Bashforth scheme for time discretization. A spatial filter of Laplace type is used by the finite volume solver to enable long simulations without suffering from late time instability problems. The numerical examples demonstrate that the hybrid solver is superior to stand-alone FD-TD in terms of accuracy and efficiency.     

Achieving spilling-friendly register file assignment for highly distributed register files

Distributed register file architectures divide registers into multiple sets, and it follows that the register files could be small. This can increase the frequency of spilling if register allocation encounters high register pressure, which will reduce the performance. That is, there is extra spilling to handle the pressure and results in performance decline. One of the factors that can produce high pressure is improper register file assignment. Register file assignment is a phase that assigns virtual registers to suitable register files and avoids communication costs. To reduce spilling in the phase of register file assignment, this paper proposes the SPIlling-FRiendly (SPIFR) method, which attempts to improve spilling by estimating the spilling cost from two aspects: assignment and spilling. We used MiBench and EEMBC benchmarks in experiments performed with the Open64-based compiler and a cycle-accurate instruction set simulator. The MiBench experimental results show that the SPIFR method improved the average cycle counts of the benchmarks by 6.0 %. For the kernels of the benchmarks, the method improved the average cycle counts by 20.5 % and reduced the average spilling ratio by 19.0 %. The results on the EEMBC benchmarks indicate that the method improved the cycle counts with the average speedup of 7.0 %, the speedup average of the kernel functions was 11.3 %, and the average reduction in the spilling ratio was 11.7 %, respectively. We conclude that the SPIFR method can reduce spilling and increase the performance.     

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

In partitioned fluid–structure interaction simulations, the flow equations and the structural equations are solved separately. As a result, a coupling algorithm is needed to enforce the equilibrium on the fluid–structure interface in cases with strong interaction. This coupling algorithm performs coupling iterations between the solver of the flow equations and the solver of the structural equations. Current coupling algorithms couple one flow solver with one structural solver. Here, a new class of multi-solver quasi-Newton coupling algorithms for unsteady fluid–structure interaction simulations is presented. More than one flow solver and more than one structural solver are used for a single simulation. The numerical experiments demonstrate that the duration of a simulation decreases as the number of solvers is increased.     

A two-port model for wave propagation along a long circular microchannel

A compact model for oscillatory flow in a long microchannel with a circular cross-section is derived from the linearised Navier–Stokes equations. The resulting two-port model includes the effects of viscosity due to rarefied gas in the slip flow regime, inertia, compressibility and losses due to heat exchange. Both an acoustic impedance T network and an acoustic admittance Π network are presented for implementation in system level and circuit simulation tools. Also, reduced T and Π networks with constant component values are given to be used in the low frequency region. They are useful in time domain simulations, too. To verify the analytical model, simulations with a harmonic finite element solver for acoustic viscous flow are performed for microchannels exploiting the axisymmetry. The simulation results with both open and closed outlet conditions are compared with the two-port model with excellent agreement. Contribution of the slip conditions and the accuracy of the simple model are demonstrated.     

Numerical Convergence Study of Nearly Incompressible,Inviscid Taylor–Green Vortex Flow

A spectral method and a fifth-order weighted essentially non-oscillatory method were used to examine the consequences of filtering in the numerical simulation of the three-dimensional evolution of nearly-incompressible, inviscid Taylor–Green vortex flow. It was found that numerical filtering using the high-order exponential filter and low-pass filter with sharp high mode cutoff applied in the spectral simulations significantly affects the convergence of the numerical solution. While the conservation property of the spectral method is highly desirable for fluid flows described by a system of hyperbolic conservation laws, spectral methods can yield erroneous results and conclusions at late evolution times when the flow eventually becomes under-resolved. In particular, it is demonstrated that the enstrophy and kinetic energy, which are two integral quantities often used to evaluate the quality of numerical schemes, can be misleading and should not be used unless one can assure that the solution is sufficiently well-resolved. In addition, it is shown that for the Taylor–Green vortex (for example) it is useful to compare the predictions of at least two numerical methods with different algorithmic foundations (such as a spectral and finite-difference method) in order to corroborate the conclusions from the numerical solutions when the analytical solution is not known.     

A Fourth Order Scheme for Incompressible Boussinesq Equations

A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation. The method is especially suitable for moderate to large Reynolds number flows. The momentum equation is discretized by a compact fourth order scheme with the no-slip boundary condition enforced using a local vorticity boundary condition. Fourth order long-stencil discretizations are used for the temperature transport equation with one-sided extrapolation applied near the boundary. The time stepping scheme for both equations is classical fourth order Runge–Kutta. The method is highly efficient. The main computation consists of the solution of two Poisson-like equations at each Runge–Kutta time stage for which standard FFT based fast Poisson solvers are used. An example of Lorenz flow is presented, in which the full fourth order accuracy is checked. The numerical simulation of a strong shear flow induced by a temperature jump, is resolved by two perfectly matching resolutions. Additionally, we present benchmark quality simulations of a differentially-heated cavity problem. This flow was the focus of a special session at the first MIT conference on Computational Fluid and Solid Mechanics in June 2001.     

A parallel Aitken-additive Schwarz waveform relaxation suitable for the grid

The objective of this paper is to describe a grid-efficient parallel implementation of the Aitken–Schwarz waveform relaxation method for the heat equation problem. This new parallel domain decomposition algorithm, introduced by Garbey [M. Garbey, A direct solver for the heat equation with domain decomposition in space and time, in: Springer Ulrich Langer et al. (Ed.), Domain Decomposition in Science and Engineering XVII, vol. 60, 2007, pp. 501–508], generalizes the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems. Although the standard Schwarz waveform relaxation algorithm has a linear rate of convergence and low numerical efficiency, it can be easily optimized with respect to cache memory access and it scales well on a parallel system as the number of subdomains increases. The Aitken-like acceleration method transforms the Schwarz algorithm into a direct solver for the parabolic problem when one knows a priori the eigenvectors of the trace transfer operator. A standard example is the linear three dimensional heat equation problem discretized with a seven point scheme on a regular Cartesian grid. The core idea of the method is to postprocess the sequence of interfaces generated by the additive Schwarz wave relaxation solver. The parallel implementation of the domain decomposition algorithm presented here is capable of achieving robustness and scalability in heterogeneous distributed computing environments and it is also naturally fault tolerant. All these features make such a numerical solver ideal for computational grid environments. This paper presents experimental results with a few loosely coupled parallel systems, remotely connected through the internet, located in Europe, Russia and the USA.     

A Numerical Method for Free-Surface Flows and Its Application to Droplet Impact on a Thin Liquid Layer

We propose a simple and practical numerical method for free surface flows. The method is based various methods, the level set method of an interface capturing method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighed line interface calculation) method of an interface tracking method, the CIP-CSL (constrained interpolation profile conservative semi-Lagrangian) method of a conservation equation solver, VSIAM3 (volume/surface integrated average based multi-moment method) of a fluid solver and the CSF (continuum surface force) model of a surface force model. The level set method and the THINC/WLIC method are combined by using a CLSVOF (coupled level set and volume-of-fluid) framework. The method is applied to Rayleigh-Taylor instability with surface tension force and droplet impact on a thin liquid layer (milk crown).     

Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and DES

The design of long-span bridges often depends on wind tunnel testing of sectional or full aeroelastic models. Some progress has been made to find a computational alternative to replace these physical tests. In this paper, an innovative computational fluid dynamics (CFD) method is presented, where the fluid-structure interaction (FSI) is solved through a self-developed code combined with an ANSYS-CFX solver. Then an improved CFD method based on block-iterative coupling is also proposed. This method can be readily used for two dimensional (2D) and three dimensional (3D) structure modelling. Detached-Eddy simulation for 3D viscous turbulent incompressible flow is applied to the 3D numerical analysis of bridge deck sections. Firstly, 2D numerical simulations of a thin airfoil demonstrate the accuracy of the present CFD method. Secondly, numerical simulations of a U-shape beam with both 2D and 3D modelling are conducted. The comparisons of aerodynamic force coefficients thus obtained with wind tunnel test results well meet the prediction that 3D CFD simulations are more accurate than 2D CFD simulations. Thirdly, 2D and 3D CFD simulations are performed for two generic bridge deck sections to produce their aerodynamic force coefficients and flutter derivatives. The computed values agree well with the available computational and wind tunnel test results. Once again, this demonstrates the accuracy of the proposed 3D CFD simulations. Finally, the 3D based wake flow vision is captured, which shows another advantage of 3D CFD simulations. All the simulation results demonstrate that the proposed 3D CFD method has good accuracy and significant benefits for aerodynamic analysis and computational FSI studies of long-span bridges and other slender structures.     

Large eddy simulation of turbulent heat transport in the Strait of Gibraltar

We develop a numerical model for large eddy simulation of turbulent heat transport in the Strait of Gibraltar. The flow equations are the incompressible Navier–Stokes equations including Coriolis forces and density variation through the Boussinesq approximation. The turbulence effects are incorporated in the system by considering the Smagorinsky model. As a numerical solver we propose a finite element semi-Lagrangian method. The solution procedure consists of combining a non-oscillatory semi-Lagrangian scheme for time discretization with the finite element method for space discretization. Numerical results illustrate a buoyancy-driven circulations along the Strait of Gibraltar and the sea-surface temperature is flushed out and move to northeast coast. The Ocean discharge and the temperature difference are shown to control the plume structure.