We Solve the World’s Toughest Free Surface CFD Problems

This article explores the science behind FLOW-3D’s accuracy, comprehensive physics and numerical methods that allow our customers to solve the toughest free surface CFD problems. FLOW-3D’s “secret sauce” of the proprietary TruVOF method, the elegance of FAVOR™ and flexible numerical options make FLOW-3D the unparalleled choice for solving tough engineering problems that involve complex multiphysics free surface flow.

The TruVOF Method

The original VOF method for tracking sharp fluid interfaces was invented by C.W. “Tony” Hirt, the founder of Flow Science and FLOW-3D, and since then has been fine-tuned and perfected for over four decades to provide the most accurate and optimized version of VOF for free-surface flows on the market. We refer to our implementation as TruVOF. The main strength of FLOW-3D’s TruVOF method is in the ability to model only the liquid phase, replacing the gas with a free surface boundary. This approach is valid when the density of the liquid is much higher than that of the surrounding gas, as is typically the case in water/air and metal/air systems. The one-fluid model greatly reduces the required computational effort, since no equations need to be solved in the gas region, and, in fact, improves the accuracy of the free surface dynamics because the interface is directly modeled as a sharp interface. That very sharp interface tracking algorithm can also be applied to model full two-fluid liquid-gas and liquid-liquid systems, with flow and thermal dynamics captured in both phases, with the gas phase treated as a fully compressible fluid.

Numerical Methods

FLOW-3D uses a variety of discretization schemes and explicit/implicit approximations of the flow equations. Sophisticated algorithms, designed to produce the most accurate and efficient solution, automatically control stability and convergence parameters at runtime, allowing the user to concentrate her attention on the physical and process aspects of the simulation. Yet, access to the numerical settings is available to an experienced user both during setup and simulation to fine-tune those parameters in really challenging cases.

Fluid Structure Interaction

FLOW-3D’s Fluid Structure Interaction (FSI) and Thermal Stress Evolution (TSE) models provide a fully coupled solution to fluid dynamics as well as solid mechanics. The former solves elastic stresses within solid components, while the latter solves them within solidified fluid regions. For fluid-structure interactions, fluid pressures, thermal gradients and body forces contribute to deformations in the solid. These deformations are then fed back into the fluid flow. The fluid computations are performed on a finite-difference Cartesian mesh and the strain-stress equations are solved on a finite-element body-fitted mesh. Currently, the model is limited to small deformations.

Heat Transfer

The heat transfer model in FLOW-3D solves full conjugate heat transfer equations, accounting for heat transfer within and between fluid, solid and void through conduction, convection and basic radiation. Both first- and second-order convection algorithms are available as are explicit and implicit numerical approximations. Heat transfer can be coupled with liquid-vapor and liquid-solid phase change.

Viscous Flows

FLOW-3D can model both Newtonian and non-Newtonian fluids. For non-Newtonian fluids the viscosity can be a function of the strain rate and/or temperature. Viscoelastic models in FLOW-3D include the Oldroyd-B model and the Giesekus model. Additional models can be implemented via user customizations of the fluid properties. Elasto-visco-platic fluids can also be modeled, in which case elastic stress is computed incrementally, allowing simulation of highly non-linear flows with large deformations over long time scales.


FLOW-3D is a uniquely powerful multiphysics tool. With its focus on free surface and multi-phase applications, it provides a complete and versatile CFD simulation platform for engineers investigating the dynamic behavior of liquids and gas in a wide range of industrial applications and physical processes, including microfluidics, nano- and bio-technology, water and environmental infrastructure, aerospace, consumer products, additive manufacturing, inkjet printing, laser welding, offshore, energy, and automotive.

Porous Media

FLOW-3D simulates both saturated and unsaturated flows within porous media. Saturated porous media flows are for situations where there is a sharp (or nearly sharp) interface between the saturated zone and the unsaturated zone, with a specific capillary pressure present at the interface. Such situations occur in groundwater flows. Unsaturated porous media flows are for situations where there is a gradual transition from the saturated zone to the unsaturated zone. In these situations, there is no set capillary pressure; the capillary pressure is a function of the current saturation level and the history of the saturation within the porous material. In both cases, different porosity, permeability and wettability (capillary pressure or capillary pressure vs. saturation) can be specified independently for each component, and permeability can be either isotropic (the same in all directions) or anisotropic (dependent on flow direction).

Turbulence Models

FLOW-3D offers a comprehensive turbulence modeling suite for fully 3-D flows, 2-D depth-averaged (shallow water) flows, and hybrid 3-D/2-D depth-averaged flows. There are eight available turbulence options in FLOW-3D: the Prandtl mixing length model, the one-equation model, the standard k-ε model, the Renormalized Group (RNG) k-ε model, the k-ω two-equation model, the LES model, and two 2-D depth-averaged shallow water turbulence models; the first of which assumes a logarithmic fully-turbulent velocity and a constant drag coefficient, and the second of which makes the drag coefficient a dynamic function of fluid depth and spatially variable surface roughness.

Gas Bubble Models

FLOW-3D has several gas bubble models which allow gas regions to exhibit a pressure-volume dependence and include phase change and heat transfer between liquid and gas, while not requiring detailed dynamic computations in the gas. These models offer big computational time savings that win many uses in microfluidic and other applications.

Industry-focused Models

In addition to the general models for fluid flow, FLOW-3D offers different sets of models developed for specialized industry applications, such as air entrainment and sediment scour for water and environmental, solidification and shrinkage for metal casting, etc.

Meshing, Geometry & CAD

Free Gridding

FLOW-3D’s approach to gridding combines the advantages of simple rectangular grids with the flexibility of deformed, body-fitted grids. Fixed grids of rectangular control elements are simple to generate and possess many desirable properties, e.g., improved accuracy, smaller demands on memory, and simpler numerical approximations. The approach is referred to as “free-gridding” because grids and geometry can be freely changed independently of one another. This feature eliminates the tedious task of generating body-fitted or finite-element grids. The flexibility and efficiency of rectangular gridding is enhanced by advanced features such as multi-block and conforming meshing. Linked, nested and partially-overlapping mesh blocks provide the means to effectively enmesh complex, multi-scale flow domains and concentrate high resolution in the areas of interest. Conforming meshes allow users to generate high quality grids that conform to specific geometric shapes or cavities, and efficiently resolve thin structures and boundary layers, without the limitations typically associated with structured rectangular gridding.


FLOW-3D incorporates a special technique, known as the FAVOR™ (Fractional Area Volume Obstacle Representation) method, which is used to define general geometric regions within the rectangular grid. The philosophy behind FAVOR™ is that numerical algorithms are based on information consisting of only one pressure, one velocity, one temperature, etc., for each control volume, making it inconsistent to use much more information to define the geometry. The FAVOR™ technique retains the simplicity of rectangular elements while representing complex geometric shapes at a level consistent with the use of averaged flow quantities within each volume element.


A simple and powerful solids modeler is packaged with FLOW-3D, or users may import geometric stereolithography (STL) files from a CAD program. FLOW-3D takes STL files that are universally exported by all CAD software available on the market. Even though FLOW-3D has a fluid-structure interaction model, where the finite volume solver for the fluid is coupled with an internal finite element solver for structural analysis, FLOW-3D also provides an interface with a variety of FEA software for a more sophisticated solid mechanics analysis. With batch processing, FLOW-3D is easily coupled with optimization tools like CAESES, HEEDS, and modeFRONTIER. FLOW-3D’s built-in mesh generator can generate body fitted finite element meshes (tetrahedral or hexahedral) for any complex shape from flow mesh, with little to no input from the user. However, the user also has the option of importing elaborate and complex finite element meshes generated with external mesh generators.

Postprocessing & Visualization

FlowSight™, FLOW-3D’s advanced postprocessing tool delivers sophisticated visualizations of FLOW-3D results. FlowSight provides modelers with superior results analysis capabilities within an intuitive user interface. Arbitrary 2D clips along spline pathways, 3D clips and transparencies, volume rendering, advanced data time series plotting and calculators, streamline and vector plots are just some of the amazing range of tools available. Combined with a rich feature set of multiple viewports and dynamic object visualization tools, using FlowSight allows engineers to make the most of their CFD results for analysis and presentation.

Licensing Structure

FLOW-3D’s licensing is flexible and offered in a variety of options. Short term licenses from one month to perpetual licenses are available on a per seat basis. Each seat can either run on shared-memory CPU cores or on distributed-memory nodes and CPU cores. FLOW-3D scales from a single CPU core, to hundreds or thousands of cores for very large simulations.

High Performance Computing and CFD in the Cloud

FLOW-3D has been available for high performance computing (HPC) on clusters for over a decade. The HPC version of FLOW-3D uses MPI (message passing interface) as well as OpenMP parallelization to achieve optimum performance on distributed memory clusters. Users with large problems can significantly reduce their runtimes by using this version on many CPU cores. To alleviate the barriers of acquiring and maintaining on-site, HPC hardware resources, FLOW-3D has been deployed in the cloud where the users can simply access a cloud workstation through their internet browser and run FLOW-3D on thousands of CPU cores in the background. The cloud workstation has full graphics that enables remote visualization, so that the user can pre- and post-process their simulation without the need for downloading large results files. The cloud offering of FLOW-3D is through the same licensing as its desktop version as well as a pay-per-use model. View benchmarks demonstrating scaling and performance metrics for different applications.