Using Graphics Processing Units to Accelerate Numerical Simulations of Interfacial Incompressible Flows

2012 ◽  
Author(s):  
Stephen R. Codyer ◽  
Mehdi Raessi ◽  
Gaurav Khanna
Keyword(s):  
Linear Algebra ◽  
Graphics Processing Units ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Surface Tension Force ◽  
Double Precision ◽  
Convergence Criteria ◽  
Time Step ◽  
Two Phase ◽  
Poisson Problem

We present a GPU accelerated numerical solver for incompressible, immiscible, two-phase fluid flows. This leads to a significant simulation speed-up and thus, the capability to have finer grid sizes and/or more accurate convergence criteria. We solve the Navier-Stokes equations, which include the surface tension force, by using a two-step projection method requiring the iterative solution to a pressure Poisson problem at each time step. However, running a serial linear algebra solver on a CPU to solve the pressure Poisson problem can take 50–99.9% of the total simulation time. To remove this bottleneck, we employ the large parallelization capabilities of GPUs by developing a double-precision parallel linear algebra solver, SCGPU, using NVIDIA’s CUDA v.4.0 libraries. The performance of SCGPU in serial simulations is presented, in addition to an evaluation of two pre-packaged GPU linear algebra solvers CUSP and CULA-sparse. We also present preliminary results of a GPU-accelerated MPI CPU flow solver.

Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 727-750 ◽  
Author(s):  
Gareth P. Williams
Keyword(s):  
Poisson Equation ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Wave Flow ◽  
Trigonometric Interpolation ◽  
Time Step ◽  
Navier Stokes Equations ◽  
The Poisson Equation

A method of numerically integrating the Navier-Stokes equations for certain three-dimensional incompressible flows is described. The technique is presented through application to the particular problem of describing thermal convection in a rotating annulus. The equations, in cylindrical polar co-ordinate form, are integrated with respect to time by a marching process, together with the solving of a Poisson equation for the pressure. A suitable form of the finite difference equations gives a computationally-stable long-term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow.Trigonometric interpolation techniques provide accurate (discretely exact) solutions to the Poisson equation. By using an auxiliary algorithm for rapid evaluation of trigonometric transforms, the proportion of computation needed to solve the Poisson equation can be reduced to less than 25% of the total time needed to’ advance one time step. Computing on a UNIVAC 1108 machine, the flow can be advanced one time-step in 2 sec for a 14 × 14 × 14 grid upward to 96 sec for a 60 × 34 × 34 grid.As an example of the method, some features of a solution for steady wave flow in annulus convection are presented. The resemblance of this flow to the classical Eady wave is noted.

Fully Lagrangian Modeling of Two-Phase Impulse Microjets

2013 ◽  
Author(s):  
Natalia Lebedeva ◽  
Alexander Osiptsov ◽  
Sergei Sazhin
Keyword(s):  
Carrier Phase ◽  
Stokes Equations ◽  
Order System ◽  
Navier Stokes ◽  
Time Step ◽  
Particle Trajectories ◽  
Two Phase ◽  
Novel Approach ◽  
Mesh Free ◽  
Lagrangian Modeling

A new fully Lagrangian approach to numerical simulation of 2D transient flows of viscous gas with inertial microparticles is proposed. The method is applicable to simulation of unsteady viscous flows with a dilute admixture of non-colliding particles which do not affect the carrier phase. The novel approach is based on a modification and combination of the full Lagrangian method for the dispersed phase, proposed by Osiptsov [1], and a Lagrangian mesh-free vortex-blob method for Navier-Stokes equations describing the carrier phase in the format suggested by Dynnikova [2]. In the combined numerical algorithm, both these approaches have been implemented and used at each time step. In the first stage, the vortex-blob approach is used to calculate the fields of velocity and spatial derivatives of the carrier-phase flow. In the second stage, using Osiptsov’s approach, particle velocities and number density are calculated along chosen particle trajectories. In this case, the problem of calculation of all parameters of both phases (including particle concentration) is reduced to the solution of a high-order system of ordinary differential equations, describing transient processes in both carrier and dispersed phases. The combined method is applied to simulate the development of vortex ring-like structures in an impulse two-phase microjet. This flow involves the formation of local zones of particle accumulation, regions of multiple intersections of particle trajectories, and multi-valued particle velocity and concentration fields. The proposed mesh-free approach enables one to reproduce with controlled accuracy these flow features without excessive computational costs.

scholarly journals Numerical simulation of compressible cavitating two-phase flows with a pressure-based solver

2017 ◽  
Author(s):  
Marco Cristofaro ◽  
Wilfried Edelbauer ◽  
Manolis Gavaises ◽  
Phoevos Koukouvinis
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Test Case ◽  
Time Step ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Liquid Phases ◽  
Flow Features ◽  
Liquid Evaporation ◽  
Semi Empirical

This work intends to study the effect of compressibility on throttle flow simulations with a pressure–based solver.The simple micro throttle geometry allows easier access for obtaining experimental data compared to a real injector, but still maintaining the main flow features. For this reasons it represents a meaningful and well reported benchmark for validation of numerical methods developed for cavitating injector flows.An implicit pressure–based compressible solver is used on the filtered Navier–Stokes equations. Thus, no stability limitation is applied on the time step. A common pressure field is computed for all phases, but different velocity fields are solved for each phase, following the multi–fluid approach. The liquid evaporation rate is evaluated with a Rayleigh–Plesset equation based cavitation model and the Coherent Structure Model is adopted as closure for the sub–grid scales in the momentum equation.The aim of this study is to show the capabilities of the pressure–based solver to deal with both vapor and liquid phases considered compressible. A comparison between experimental results and compressible simulations is presented. Time–averaged vapor distribution and velocity profiles are reported and discussed.  The distribution of pressure maxima on the surface and the results from a semi–empirical erosion model are in good agreement with the erosion locations observed in the experiments. This test case aims to represent a benchmark for furtherapplication of the methodology to industrial relevant cases.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4629

scholarly journals COMPUTATIONAL FLUID DYNAMIC ANALYSIS OF HIGHWAY BRIDGES EXPOSED TO HURRICANE WAVES

2012 ◽  
Vol 1 (33) ◽  
pp. 70 ◽  
Author(s):  
Mehrdad Bozorgnia ◽  
Jiin-Jen Lee
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Highway Bridges ◽  
Numerical Code ◽  
Time Step ◽  
Computational Fluid Dynamic Analysis ◽  
Two Phase ◽  
Simulation Results

In present paper, numerical code STAR CCM+ by CD-adapco which works based on compressible two-phase Navier Stokes equations is used to evaluate hydrodynamic forces exerted on prototype of I10 Bridge over Escambia Bay which was extensively damaged during Hurricane Ivan. Volume of Fluid (VOF) is used to capture dynamic free surface which is well suited for simulating complex discontinuous free surface associated with wave-deck interactions. 2D and 3D models were setup and properly configured. Simulations were conducted on High performance Computing and Communication Center (HPCC) at University of Southern California. Simulation results are compared to experimental data available from Hinsdale Wave Laboratory at Oregon State University. Comparison of experimental data to simulation results show the importance of proper mesh size and time step choice on accuracy of horizontal and vertical hydrodynamic force predictions applied to bridge superstructure.

scholarly journals Well-posedness of a diffuse-interface model for two-phase incompressible flows with thermo-induced Marangoni effect

2016 ◽  
Vol 28 (3) ◽  
pp. 380-434 ◽  
Author(s):  
HAO WU
Keyword(s):  
Existence And Uniqueness ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Marangoni Effect ◽  
Strong Solutions ◽  
Diffuse Interface ◽  
Fluid Viscosity ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Two Phase

We investigate a non-isothermal diffuse-interface model that describes the dynamics of two-phase incompressible flows with thermo-induced Marangoni effect. The governing PDE system consists of the Navier--Stokes equations coupled with convective phase-field and energy transport equations, in which the surface tension, fluid viscosity and thermal diffusivity are allowed to be temperature dependent functions. First, we establish the existence and uniqueness of local strong solutions when the spatial dimension is two and three. Then, in the two-dimensional case, assuming that theL∞-norm of the initial temperature is suitably bounded with respect to the coefficients of the system, we prove the existence of global weak solutions as well as the existence and uniqueness of global strong solutions.

scholarly journals URANSE-Based Numerical Prediction for the Free Roll Decay of the DTMB Ship Model

2021 ◽  
Vol 9 (5) ◽  
pp. 452
Author(s):  
Adham Bekhit ◽  
Florin Popescu
Keyword(s):  
Experimental Data ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Roll Angle ◽  
Navier Stokes ◽  
Special Focus ◽  
Time Step ◽  
Two Phase ◽  
Ship Model ◽  
Richardson Extrapolation Method

In the present study, Computational Fluid Dynamics (CFD) is used to investigate the roll decay of the benchmark surface combatant DTMB-5512 ship model appended with bilge keels, sailing in calm water at different speeds (Fr = 0.0, 0.138, 0.2, 0.28 and 0.41) and with different initial roll angles. The numerical simulations are carried out using the viscous flow solver ISIS-CFD of the FINETM/Marine software provided by NUMECA. The solver uses the finite volume method to build the spatial discretization of the transport equation to solve the unsteady Reynolds-Averaged Navier–Stokes equations. Two-phase flow approach is applied to model the air–water interface, where the free surface is captured using the volume of fluid method. The closure to turbulence is achieved by making use of the blended Menter shear stress transport and the explicit algebraic Reynolds stress models. First, a systematic validation against the experimental data at medium speed and initial roll angle of 10° are performed; then, the effect of the initial roll angle and ship speed is later studied. Numerical errors and uncertainties are assessed using grid and time step convergence study based on Richardson Extrapolation method. A special focus on the flow in the vicinity of the bilge keels during the simulation is also investigated and presented in the form of velocity contours and vortical structure formations. The resemblance between the CFD results and experimental data for roll motion and flow characteristics are within a satisfactory congruence; however, some discrepancies are recorded for the over predicted roll amplitudes in the second and, sometimes, the third roll cycle, which appeared mostly in the cases with high initial roll angles.

scholarly journals Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios

2020 ◽  
Author(s):  
Mohamed EL OUAFA ◽  
stephane vincent ◽  
Vincent Le Chenadec
Keyword(s):  
Augmented Lagrangian ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Staggered Grid ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Time Step ◽  
Two Phase ◽  
Flow Equations ◽  
Fully Coupled

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods.

scholarly journals Assessment of Discretization Uncertainty Estimators Based On Grid Refinement Studies

2021 ◽  
Author(s):  
Luis Eca ◽  
Guilherme Vaz ◽  
Martin Hoekstra ◽  
Scott Doebling ◽  
Robert Singleton ◽  
...  
Keyword(s):  
Incompressible Flows ◽  
Turbulence Models ◽  
Double Precision ◽  
Grid Refinement ◽  
Convergence Criteria ◽  
Data Set ◽  
Local Flow ◽  
Uncertainty Estimates ◽  
Wide Range ◽  
Naca 0012

Abstract This paper presents the assessment of the performance of 9 discretization uncertainty estimates based on grid refinement studies including methods that use grid triplets and others that use a largest number of data points, which in the present study was set to five. The uncertainty estimates are performed for the data set proposed for the 2017 ASME Workshop on Estimation of Discretization Errors including functional and local flow quantities from the two-dimensional incompressible flows over a flat plate and the NACA 0012 airfoil. The data were generated with a RANS solver using three eddy-viscosity turbulence models with double precision and sufficiently tight iterative convergence criteria to ensure that the numerical error is dominated by the discretization error. The use of several geometrically similar grid sets with different near-wall cell sizes lead to a wide range of convergence properties for the selected flow quantities. The evaluation of uncertainty estimates is based on the ratio of the estimated uncertainty over the "exact error" that is obtained from an "exact solution" obtained from extra grid sets significantly more refined than those used to generate the Workshop data. Although none of the methods tested fulfilled the goal of bounding the "exact error" 95 times out of 100 that was tested, the results suggest that the methods tested are useful tools for the assessment of the numerical uncertainty of practical numerical simulations even for cases where it is not possible to generate data in the "asymptotic range".

scholarly journals Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 23
Author(s):  
Mohamed El Ouafa ◽  
Stephane Vincent ◽  
Vincent Le Chenadec
Keyword(s):  
Augmented Lagrangian ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Staggered Grid ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Time Step ◽  
Two Phase ◽  
Flow Equations ◽  
Fully Coupled

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods.

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