Robust and Efficient Wave Simulations on Deforming Meshes

The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real‐time environments. In order to achieve our goal, we reduce the problem from a three‐ to a two‐dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.     

A multigrid fluid pressure solver handling separating solid boundary conditions

We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation’s pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time, because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios, including nonaxis-aligned containers and moving solids in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to solids. Our measurements show, that the convergence rate of our LCP solver is close to that of a standard multigrid solver.     

Combined finite volume–finite element method for shallow water equations

This paper is concerned with solving the viscous and inviscid shallow water equations. The numerical method is based on second-order finite volume–finite element (FV–FE) discretization: the convective inviscid terms of the shallow water equations are computed by a finite volume method, while the diffusive viscous terms are computed with a finite element method. The method is implemented on unstructured meshes. The inviscid fluxes are evaluated with the approximate Riemann solver coupled with a second-order upwind reconstruction. Herein, the Roe and the Osher approximate Riemann solvers are used respectively and a comparison between them is made. Appropriate limiters are used to suppress spurious oscillations and the performance of three different limiters is assessed. Moreover, the second-order conforming piecewise linear finite elements are used. The second-order TVD Runge–Kutta method is applied to the time integration. Verification of the method for the full viscous system and the inviscid equations is carried out. By solving an advection–diffusion problem, the performance assessment for the FV–FE method, the full finite volume method, and the discontinuous Galerkin method is presented.     

Performance of a new partitioned procedure versus a monolithic procedure in fluid–structure interaction

Fluid–structure interaction (FSI) can be simulated in a monolithic way by solving the flow and structural equations simultaneously and in a partitioned way with separate solvers for the flow equations and the structural equations. A partitioned quasi-Newton technique which solves the coupled problem through nonlinear equations corresponding to the interface position is presented and its performance is compared with a monolithic Newton algorithm. Various structural configurations with an incompressible fluid are solved, and the ratio of the time for the partitioned simulation, when convergence is reached, to the time for the monolithic simulation is found to be between 1/2 and 4. However, in this comparison of the partitioned and monolithic simulations, the flow and structural equations have been solved with a direct sparse solver in full Newton–Raphson iterations, only relatively small problems have been solved and this ratio would likely change if large industrial problems were considered or if other solution strategies were used.     

An Efficient Solver for Two‐way Coupling Rigid Bodies with Incompressible Flow

We present an efficient solver for monolithic two‐way coupled simulation of rigid bodies with incompressible fluids that is robust to poor conditioning of the coupled system in the presence of large density ratios between the solid and the fluid. Our method leverages ideas from the theory of Domain Decomposition, and uses a hybrid combination of direct and iterative solvers that exploits the low‐dimensional nature of the solid equations. We observe that a single Multigrid V‐cycle for the fluid equations serves as a very effective preconditioner for solving the Schur‐complement system using Conjugate Gradients, which is the main computational bottleneck in our pipeline. We use spectral analysis to give some theoretical insights behind this observation. Our method is simple to implement, is entirely assembly‐free besides the solid equations, allows for the use of large time steps because of the monolithic formulation, and remains stable even when the iterative solver is terminated early. We demonstrate the efficacy of our method on several challenging examples of two‐way coupled simulation of smoke and water with rigid bodies. To illustrate that our method is applicable to other problems, we also show an example of underwater bubble simulation.     

Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method

The development and validation of a parallel unstructured tetrahedral non-nested multigrid (MG) method for simulation of unsteady 3D incompressible viscous flow is presented. The Navier-Stokes solver is based on the artificial compressibility method (ACM) and a higher-order characteristics-based finite-volume scheme on unstructured MG. Unsteady flow is calculated with an implicit dual time stepping scheme. The parallelization of the solver is achieved by a MG domain decomposition approach (MG-DD), using the Single Program Multiple Data (SPMD) programming paradigm. The Message-Passing Interface (MPI) Library is used for communication of data and loop arrays are decomposed using the OpenMP standard. The parallel codes using single grid and MG are used to simulate steady and unsteady incompressible viscous flows for a 3D lid-driven cavity flow for validation and performance evaluation purposes. The speedups and efficiencies obtained by both the parallel single grid and MG solvers are reasonably good for all test cases, using up to 32 processors on the SGI Origin 3400. The parallel results obtained agree well with those of serial solvers and with numerical solutions obtained by other researchers, as well as experimental measurements.     

Randomized constraint solvers: a comparative study

The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compared the effectiveness of a symbolic solver (CVC3), a random solver, two heuristic search solvers, and seven hybrid solvers (i.e. mix of random, symbolic, and heuristic solvers). We evaluated the solvers on a benchmark generated with a concolic execution of 9 subjects. The performance of each solver was measured by its precision, which is the fraction of constraints that the solver can find solution out of the total number of constraints that some solver can find solution. As expected, symbolic solving subsumes the other approaches for the 4 subjects that only generate decidable constraints. For the remaining 5 subjects, which contain undecidable constraints, the hybrid solvers achieved the highest precision (fraction of constraints that a solver can find a solution out of the total number of satisfiable constraints). We also observed that the solvers were complementary, which suggests that one should alternate their use in iterations of a concolic execution driver.     

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.     

Solution properties and approximate Riemann solvers for two-layer shallow flow models

The 4 × 4 system of governing equations for two-layer shallow flow models is known to exhibit particular behaviours such as loss of hyperbolicity under certain flow configurations. An eigenvalue analysis of the conservation part of the equations shows that the loss of hyperbolicity is due only to the reaction exerted by each fluid onto the other at the interface between the fluids. Three Riemann solvers derived from the HLL formalism are presented. In the first solver, the pressure-induced terms are accounted for by the source term; in the second solver, they are incorporated into the fluxes; the third solver uses the same formulation as the first, except that the mass and momentum balance for the bottom layer are replaced with the balance equations for the system formed by the two layers as a whole. Numerical results using the three solvers are presented for (1) static conditions such as two fluids of identical densities at rest above each other, (2) dam-break flows involving the collapse of a body of light fluid over a uniform layer of a denser fluid, and (3) Liska and Wendroff’s ill-posed test cases [24] involving two-layer flows over a topographic bump. The three solvers produce quasi-undistinguishable results for the dam-break flows, and produce sharp solutions over the full range of density ratio, from 0 to 1. However, only the third solver allows a strict preservation of static configurations. Moreover, a method is proposed to assess the convergence of the numerical solutions in the configurations for which no analytical solution can be obtained.     

Transonic drag prediction on a DLR-F6 transport configuration using unstructured grid solvers

A second international AIAA Drag Prediction Workshop (DPW-II) was organized and held in Orlando Florida on June 21-22, 2003. The primary purpose was to investigate the code-to-code uncertainty, address the sensitivity of the drag prediction to grid size and quantify the uncertainty in predicting nacelle/pylon drag increments at a transonic cruise condition. This paper presents an in-depth analysis of the DPW-II computational results from three state-of-the-art unstructured grid Navier-Stokes flow solvers exercised on similar families of tetrahedral grids. The flow solvers are USM3D - a tetrahedral cell-centered upwind solver, FUN3D - a tetrahedral node-centered upwind solver, and NSU3D - a general element node-centered central-differenced solver. Overall, grid refinement did not consistently improve the correlation with experimental data for either the wing/body or the wing/body/nacelle pylon configuration. Although, the range in total drag for the wing/body fine grids was only 5 counts, a code-to-code comparison of surface pressures and surface restricted streamlines indicated that the three solvers were not all converging to the same flow solutions- different shock locations and separation patterns were evident. Similarly, the wing/body/nacelle/pylon solutions did not appear to be converging to the same flow solutions. Although the absolute values of total drag predicted by two of the solvers for the medium and fine grids did not compare well with the experiment, the incremental drag predictions were within ±3 counts of the experimental data. Although, the sources of code-to-code variation in force and moment predictions for the three unstructured grid codes have not yet been identified, the current study reinforces the necessity of applying multiple codes to the same application to assess uncertainty.     

Implementation of density-based solver for all speeds in the framework of OpenFOAM

In the framework of open source CFD code OpenFOAM, a density-based solver for all speeds flow field is developed. In this solver the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) solver for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this solver possesses high accuracy and the solver developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned solvers with and without the dual time scheme. Nonetheless, the solvers described in this paper reproduce the main features of this flow, including the evolution of the initial transient.     

Flow simulation in Electro-Static-Precipitator (ESP) ducts with turning vanes

Flow simulation in inlet ducts along with several turning vanes used in electrostatic precipitator (ESP) are analysed to understand the flow pattern at its exit locations. The geometry of inlet duct has been extracted from the Plant Design Manufacturing System (PDMS) and refined with turning vanes placed at several locations. The domain of duct geometry around turning vanes are decomposed with several volumes and filled with hexahedral elements with the help of stat-of-art mesh generator - Hypermesh. The resulting computational grid has been used in TASCflow solver to predict its flow pattern in the duct. Simulation for the specified conditions predicts uneven flow distribution in the ESP inlet duct. Due to large flow recirculation and turbulent losses in the duct, non-uniform averaged mass flow rates are noticed at duct exit locations. Simulation results suggest that the improvement of flow distribution in the duct through optimization can be tried by placing more turning/splitter vanes in the inlet duct. In order to ensure that the results obtained from TASCflow are meaningful and in right direction, in the absence of measurement data, simulation was benchmarked with other industry standard commercial flow solvers. The observations made from these popular solvers confirm the findings obtained using the TASCflow solver. The analysis with multiple solvers indicates that Fluent provides quick results, while better visualization can be made using CFX solver. The Star-CD solver, which captures the turbulent losses accurately takes more time for convergence provides alternatives.     

Application of single-level,pointwise algebraic,and smoothed aggregation multigrid methods to direct numerical simulations of incompressible turbulent flows

Single- and multi-level iterative methods for sparse linear systems are applied to unsteady flow simulations via implementation into a direct numerical simulation solver for incompressible turbulent flows on unstructured meshes. The performance of these solution methods, implemented in the well-established SAMG and ML packages, are quantified in terms of computational speed and memory consumption, with a direct sparse LU solver (SuperLU) used as a reference. The classical test case of unsteady flow over a circular cylinder at low Reynolds numbers is considered, employing a series of increasingly fine anisotropic meshes. As expected, the memory consumption increases dramatically with the considered problem size for the direct solver. Surprisingly, however, the computation times remain reasonable. The speed and memory usage of pointwise algebraic and smoothed aggregation multigrid solvers are found to exhibit near-linear scaling. As an alternative to multi-level solvers, a single-level ILUT-preconditioned GMRES solver with low drop tolerance is also considered. This solver is found to perform sufficiently well only on small meshes. Even then, it is outperformed by pointwise algebraic multigrid on all counts. Finally, the effectiveness of pointwise algebraic multigrid is illustrated by considering a large three-dimensional direct numerical simulation case using a novel parallelization approach on a large distributed memory computing cluster.     

Coupling of a nonlinear finite element structural method with a Navier-Stokes solver

A new three-dimensional viscous aeroelastic solver is developed in the present work. A well validated full Navier-Stokes code is coupled with a nonlinear finite element plate model. Implicit coupling between the computational fluid dynamics and structural solvers is achieved using a subiteration approach. Computations of several benchmark static and dynamic plate problems are used to validate the finite element portion of the code. This coupled aeroelastic scheme is then applied to the problem of three-dimensional panel flutter. Inviscid and viscous supersonic results match previous computations using the same aerodynamic method coupled with a finite difference structural solver. For the case of subsonic flow, multiple solutions consisting of static, upward and downward deflections of the panel are discussed. The particular solution obtained is shown to be sensitive to the cavity pressure specified underneath the panel.     

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.     

基于INTESIM-GISCI的流固耦合 仿真软件技术及应用

为突破传统商业软件流固耦合分析仅局限于内部预先集成的流体和结构求解器的约束,使流固耦合分析更具开放性和可拓展性,以耦合驱动程序INTESIM GISCI为框架体系,在开源流体求解器SU2的源代码上加入时间同步点和相关函数功能形成INTESIM-SU2,使INTESIM-SU2可以与原有的结构求解器INTESIM-Structure通过耦合界面传递数据的方式进行耦合分析,从而实现基于耦合驱动程序INTESIM-GISCI的流固耦合仿真软件开发。将多个流固耦合分析案例与其他商业软件进行对比,证明基于INTESIM-GISCI的流固耦合仿真软件可广泛应用于实际工程问题的仿真分析。     

Wake Synthesis For Shallow Water Equation

In fluid animation, wake is one of the most important phenomena usually seen when an object is moving relative to the flow. However, in current shallow water simulation for interactive applications, this effect is greatly smeared out. In this paper, we present a method to efficiently synthesize these wakes. We adopt a generalized SPH method for shallow water simulation and two way solid fluid coupling. In addition, a 2D discrete vortex method is used to capture the detailed wake motions behind an obstacle, enriching the motion of SWE simulation. Our method is highly efficient since only 2D simulation is required. Moreover, by using a physically inspired procedural approach for particle seeding, DVM particles are only created in the wake region. Therefore, very few particles are required while still generating realistic wake patterns. When coupled with SWE, we show that these patterns can be seen using our method with marginal overhead.     

A two-level computational graph method for the adjoint of a finite volume based compressible unsteady flow solver

The adjoint method is a useful tool for finding gradients of design objectives with respect to system parameters for fluid dynamics simulations. But the utility of this method is hampered by the difficulty in writing an efficient implementation for the adjoint flow solver, especially one that scales to thousands of cores. This paper demonstrates a Python library, called adFVM, that can be used to construct an explicit unsteady flow solver and derive the corresponding discrete adjoint flow solver using automatic differentiation (AD). The library uses a two-level computational graph method for representing the structure of both solvers. The library translates this structure into a sequence of optimized kernels, significantly reducing its execution time and memory footprint. Kernels can be generated for heterogeneous architectures including distributed memory, shared memory and accelerator based systems. The library is used to write a finite volume based compressible flow solver. A wall clock time comparison between different flow solvers and adjoint flow solvers built using this library and state of the art graph based AD libraries is presented on a turbomachinery flow problem. Performance analysis of the flow solvers is carried out for CPUs and GPUs. Results of strong and weak scaling of the flow solver and its adjoint are demonstrated on subsonic flow in a periodic box.     

A large scale parallel fluid-structure interaction computing platform for simulating structural responses to a detonation shock

Due to the intrinsic nature of multi-physics, it is prohibitively complex to design and implement a simulation software platform for study of structural responses to a detonation shock. In this article, a partitioned fluid-structure interaction computing platform is designed for parallel simulating structural responses to a detonation shock. The detonation and wave propagation are modeled in an open-source multi-component solver based on OpenFOAM and blastFoam, and the structural responses are simulated through the finite element library deal.II. To capture the interaction dynamics between the fluid and the structure, both solvers are adapted to preCICE. For improving the parallel performance of the computing platform, the inter-solver data is exchanged by peer-to-peer communications and the intermediate server in conventional multi-physics software is eliminated. Furthermore, the coupled solver with detonation support has been deployed on a computing cluster after considering the distributed data storage and load-balancing between solvers. The 3D numerical result of structural responses to a detonation shock is presented and analyzed. On 256 processor cores, the speedup ratio of the simulations for a detonation shock reach 178.0 with 5.1 million of mesh cells and the parallel efficiency achieve 69.5%. The results demonstrate good potential of massively parallel simulations. Overall, a general-purpose fluid-structure interaction software platform with detonation support is proposed by integrating open source codes. And this work has important practical significance for engineering application in fields of construction blasting, mining, and so forth.