Solvers
Suite of finite element and multibody dynamics solvers for design and optimization.
Altair OptiStruct
OptiStruct is a state-of-the-art finite element solver for linear and nonlinear structural problems. It employs implicit integration schemes for static and dynamic problems. Besides mechanical loading, heat transfer coupled with structures is also available.
OptiStruct is designed with optimization at the core. The majority of solution sequences are available for optimization. A wide range of design problems can be solved addressing concept design and design fine tuning. In addition, Altair Radioss and Altair MotionSolve have been integrated to address multi-disciplinary optimization involving crash and impact, and multibody systems, respectively. The optimization capabilities of OptiStruct are innovative and market-leading.
Analysis applications of OptiStruct include Automotive powertrain durability and vibrations, vehicle interior acoustics, vibrations of satellites, durability of heavy-duty and off-road vehicles, component stress and vibrations analysis, detailed finite element analysis of airplane structures, random vibrations of ships and buildings, structural behavior of composite wings, buckling behavior, and many other advanced engineering applications.
- Structural Analysis
- Linear Static Analysis
- Linear Buckling Analysis
- Small Displacement Nonlinear Analysis
- Large Displacement Nonlinear Static Analysis
- Normal Modes Analysis
- Frequency Response Analysis
- Complex Eigenvalue Analysis
- Brake Squeal Analysis
- Random Response Analysis
- Response Spectrum Analysis
- Linear Transient Response Analysis
- Nonlinear Transient Response Analysis
- Explicit Nonlinear Dynamic Analysis (Radioss Integration)
- Thermal Analysis
- Linear Steady-State Heat Transfer Analysis
- Linear Transient Heat Transfer Analysis
- Nonlinear Steady-State Heat Transfer Analysis
- Contact-based Thermal Analysis
- One Step Transient Thermal Stress Analysis
- Acoustic Analysis
- Coupled Frequency Response Analysis of Fluid-Structure Models
- Radiated Sound Analysis
- Fatigue Analysis
- Stress-Life method
- Strain-Life method
- Dang Van Criterion (Factor of Safety)
- Random Response Fatigue Analysis
- Rotor Dynamics
- Fast equation solver
- Sparse matrix solver
- Iterative PCG solver
- Lanczos eigensolver
- SMP parallelization
- DMIG input
- AMLS interface
- FastFRS method
- FastFRS interface
- Advanced element formulations
- Triangular, quadrilateral, first and second order shells
- Laminated shells
- Hexahedron, pyramid, tetrahedron first and second order solids
- Bar, beam, bushing, and rod elements
- Spring, mass, and damping scalar elements
- Mesh independent gap and weld elements
- Rigid elements
- Concentrated and non-structural mass
- Direct matrix input
- Geometric element quality check
- Local coordinate systems
- Multi-point constraints
- Contact, tie interfaces
- Prestressed analysis
- Linear-elastic materials
- Isotropic
- Anisotropic
- Orthotropic
- Nonlinear materials
- Elastoplastic
- Hyperelastic
- Viscoelastic
- Material consistency checks
- Ground check for unintentionally constrained rigid body modes.
- Parts and Instances
- Subcase Specific Modeling
- Direct Matrix Input (Superelements)
- Direct Matrix Input
- Creating Superelements
- Component Dynamic Analysis
- Flexible Body Generation
- Poroelastic Materials
A typical set of finite elements including shell, solid, bar, scalar, and rigid elements as well as loads and materials are available for modeling complex events.
- Kinematics
- Dynamics
- Static
- Quasi-static
- Linearization
All typical types of constraints like joints, gears, couplers, user-defined constraints, and high-pair joints can be defined. High pair joints include point-to-curve, point-to-surface, curve-to-curve, curve-to-surface, and surface-to-surface constraints. They can connect rigid bodies, flexible bodies, or rigid and flexible bodies. For this multibody dynamics solution, the power of Altair MotionSolve has been integrated with OptiStruct.
- Structural Design and Optimization
- Structural design tools include topology, topography, and free-size optimization. Sizing, shape and free shape optimization are available for structural optimization.
- Topology Optimization
- Topology optimization generates an optimized material distribution for a set of loads and constraints within a given design space. The design space can be defined using shell or solid elements, or both. The classical topology optimization set up solving the minimum compliance problem, as well as the dual formulation with multiple constraints are available. Constraints on von Mises stress and buckling factor are available with limitations. Manufacturing constraints can be imposed using a minimum member size constraint, draw direction constraints, extrusion constraints, symmetry planes, pattern grouping, and pattern repetition.
- Topography Optimization
- For thin-walled structures, beads or swages are often used as reinforcement features. For a given set of bead dimensions, OptiStruct's topography optimization technology will generate innovative design proposals with the optimal bead pattern and location for reinforcement to meet certain performance requirements. Typical applications include panel stiffening and managing frequencies.
- Size and Shape Optimization
- General size and shape optimization problems can be solved. Variables can be assigned to perturbation vectors, which control the shape of the model. Variables can also be assigned to properties, which control the thickness, area, moments of inertia, stiffness, and non-structural mass of elements in the model. All of the variables supported by OptiStruct can be assigned using Altair HyperMesh. Shape perturbation vectors can be created using HyperMorph.
- Multibody Dynamics Analysis
- Different solution sequences for the analysis of mechanical systems are available; these include Kinematics, Dynamics, Static, and Quasi-static solutions. Flexible bodies can be derived from any finite element model defined in OptiStruct.
For more information, reference the OptiStruct help manual.
Altair Radioss
Radioss is a leading structural analysis solver for highly nonlinear problems under dynamic loadings. It is highly differentiated for Scalability, Quality and Robustness, and consists of features for multi-physics simulation and advanced materials such as composites. Radioss is used across all industries worldwide to improve the crashworthiness, safety, and manufacturability of structural designs. For over 25 years, Radioss has established itself as a leader and an Industry standard for automotive crash and impact analysis.
- Explicit dynamic analysis
- Linear and nonlinear implicit static analysis
- Transient heat transfer and thermo-mechanical coupling
- Explicit Arbitrary Euler-Lagrangian (ALE) formulation
- Explicit Computational Fluid Dynamics (CFD)
- Smooth Particle Hydrodynamics (SPH)
- Incremental sheet metal stamping analysis with mesh adaptivity
- Normal modes analysis
- Linear and nonlinear buckling analysis
For more information, reference the Radioss help manual.
Altair MotionSolve
MotionSolve is a state-of-the-art multibody dynamics solver that is included in the Altair HyperWorks package. MotionSolve enables you to create realistic, physics-based simulations of sophisticated mechanical systems and includes a wide array of customization capabilities. MotionSolve has been successfully used to model and simulate a broad range of systems including automobile suspensions, aircraft landing gears, biomedical devices, and satellite launch systems. With a variety of integrators, support of for co-simulation, multiphysics and a special focus on flexible body modeling, MotionSolve is setup to cover the range of simulation needs for MBS, some of which include linear and vibration studies, stress and durability evaluation, load extraction from the multibody system, effort estimation for the multibody system, packaging studies and simulating models that encompass more than one kind of physics.
- Benefits
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- Robust, fast and accurate solving capability for a full range of MBS applications
- An encompassing array of standard and advanced modeling elements as well as kinematic, static/quasi-static, transient and linear solution types
- Ability to directly reuse ADAMS .adm/.acf files, functions and user subroutine source code
- Support and easy to setup co-simulation with Altair Activate, Altair AcuSolve, MATLAB Simulink and Fluidon DSH Plus
- No need to compile user subroutines with MotionSolve’s support of Python and MATLAB scripted user subs (and support for C++/FORTRAN user sub syntax)
- Customizable at several levels including custom elements, functions, messaging, and results
For more information, reference the MotionSolve help manual.
Altair HyperXtrude
- Metal Extrusion
- Polymer Extrusion
- Metal Rolling
- Billet Forging
- Friction Stir Welding
- Resin Transfer Molding
All these solvers are supported by easy to use interfaces under Manufacturing Solutions.
- Benefits for Metal Extrusion
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- Direct and indirect extrusion
- Solid and hollow profile extrusion·
- Single and multi-hole dies
- Multi-cycle analysis
- Bearing profile optimization
- Nose cone prediction
- Transverse weld length
- Microstructure prediction
- Weld strength prediction
- Tool deflection analysis
- Billet skin and product quality
- Support for commonly used material models
- Extrusion of super alloys with glass pad lubrication
- User-defined function of material models and results
- Coupled extrusion and tool deflection analysis
- Benefits for Polymer Extrusion
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- Sheet extrusion
- Profile extrusion
- Coextrusion of seals
- Coextrusion of tires
- Hollow and solid profiles
- Calibrator analysis
- Tube extrusion
- Runner balancing analysis
- Support for commonly used material models
- Viscoelastic model
- Ability to include heat transfer and stress work converted to heat
- Prediction of profile deformation
- Deformation of material interfaces between layers coextrusion
- Ability to include inserts in analysis
- Residence time computation
- Tool deflection analysis
- User-defined function of material models and results
- Benefits for Metal Rolling
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- Prediction of slab deformation
- Tool deflection analysis with Radioss
- Heat transfer and temperature dependence of flow stress
- Support for commonly used material models
- User-defined function of material model and results
- Benefits for Billet Forging
- Billet forging is used to change the shape of cast billet to a desired
cross-section and more importantly achieve a desired microstructure.
Following features supported by the solver makes it a valuable tool for
billet forging simulation.
- Validate and optimize forging sequence
- Compute forces on tool components
- Predict microstructure changes
- Benefits for Stir Welding
- Friction stir welding is solid state welding process that can join
dissimilar metals
- Compute forces acting on tool
- Tool deflection analysis
- Understand mixing and heat transfer in heat affected zone
- Benefits for Resin Transfer Molding
- Resin transfer molding and its variants are used for manufacturing
composites.
- Resin flow front simulation
- Fill time prediction
- Effects of heat transfer in filling and curing
- Air modeled as compressible material to consider vacuum effects
- Curing kinetics
- Gravity effects on filling
- Local coordinate system for preform material data
For more information, reference the HyperXtrude help manual.
Altair Manufacturing Solver
Altair Manufacturing Solver is a state-of-the-art solver suite for manufacturing applications built on a parallel, modular and extensible framework that is suitable for simulations of manufacturing processes. The current version of Manufacturing Solver includes a casting solver that is used under Altair Inspire Cast and an injection molding solver that has an interface in Altair SimLab.
- Casting Simulation: Supported Features
- Metal casting is a widely used manufacturing process used to mold metal
into a desired shape. This is achieved by pouring a liquid metal into a
mold and cooling it to solidify the part. There are many varieties of
casting processes that depend on how the molten metal is delivered into
the mold, the type of material used to make the mold, and the cooling
techniques. The casting solver supports the following features:
- Supported common casting techniques
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- High pressure die casting
- Low pressure die casting
- Investment casting
- Gravity sand and die casting
- Gravity tilt pouring
- Gravity tilt pouring with crucible
- Gravity with constant liquid level on the sprue
- High pressure die casting with shot sleeve
- Cycling
- Supported standard casting components
- The solver supports the modeling of standard casting
components, such as:
- Core
- Chiller
- Riser
- Isothermal and exothermal sleeves
- Overflow
- Mold
- Cooler
- Filter
- Shot sleeve
- Crucible
- Supported computed results
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- Flow Front
- Velocity
- Pressure
- Temperature
- Cold Shuts
- Air Entrapment
- Flow length
- Mold Erosion
- Solid Fraction evolution
- Shrinkage porosity
- Pipe shrinkage
- Solidification Modulus
- Niyama
- Microporosity
- Solidification time
- Modeling Simulation: Supported Features
- Injection molding is one of the most common processes used for the
production of polymer parts. This is a cyclic process and often used
with thermoplastic polymers. A polymer in the form of pellets is mixed
with other additives, then heated to a melt state, and finally
pressurized in a single screw extruder. This pressurized polymer melt is
injected into the mold at a high flow rate to fill the mold cavities.
These cavities are made in the form of the final part accounting for the
shrinkage, and then the mold is cooled and the part is ejected from the
mold as soon as it is stable enough for ejection. This is a cyclic
process and this sequence repeats. Altair Manufacturing Solver is used
for simulating the injection molding process. The following features are
supported:
- Supported solution sequences
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- Filling
- Filling + Cooling
- Filling + Cooling + Warpage
- Cooling
- Cooling + Warpage
- Filling + Packing
- Filling + Packing + Cooling
- Filling + Packing + Cooling + Warpage
- Support for fiber orientation analysis
- Fiber orientation analysis is supported and can be optionally turned on.
- Filling solution module
- The filling solution module supports:
- Velocity driven filling
- Velocity/pressure (VP) switch over
- Final pressure driven filling
- Gates can be timed with table data
- Supported packing stage phases
- The packing stage includes both packing and holding phases.
- Model support
- The solver can support models that contain:
- Complete or partial runner system
- Single or multi-cavity molds
- Analysis with or without mold plates and mold inserts
- Analysis with or without part inserts
- Symmetry conditions
- Supported computed results
-
- Air traps
- Density
- Fill time
- Pressure
- Temperature
- Velocity
- Maximum velocity
- Strain rate
- Weld surface
- Viscosity
- Sink marks
- Fiber orientation tensor
- Warpage - displacement
- Warpage - stresses
Altair AcuSolve
AcuSolve is a leading general-purpose finite element based Computational Fluid Dynamics (CFD) flow solver with superior robustness, speed, and accuracy. AcuSolve can be used by designers and research engineers with all levels of expertise to obtain quality solutions quickly without iterating on solution procedures.
AcuSolve is based on the Galerkin/Least-Squares (GLS) finite element formulation, which provides second order accuracy for spatial discretization of all variables and utilizes tightly controlled numerical diffusion operators to obtain stability and maintain accuracy. Since AcuSolve obtains rapid nonlinear convergence within each time step, temporal accuracy is achieved in practice. AcuSolve has a very rich mathematical foundation, translating into superb numerical behavior.
AcuSolve consists of multiple features to easily solve the largest and most complex mission critical industrial problems spanning a wide range of physics such as steady and unsteady flows, conjugate heat transfer including radiation in semi-transparent media, solar radiation, nucleate boiling, multiphase flow, moving meshes and rigid body dynamics, shape and parametric optimization, etc.
AcuSolve is based on an efficient parallel architecture that provides distributed, shared and hybrid parallel operation in addition to GPU acceleration.
AcuSolve can be coupled with external codes such as OptiStruct, Flux, MotionSolve, and EDEM to perform multiphysics analysis of complex scenarios in an efficient manner.
- The key benefits of AcuSolve include:
-
- Robustness: Most problems are solved on the first attempt.
- Speed: Fully coupled solver on shared memory and distributed parallel systems in addition to GPU acceleration.
- Accuracy: Highly accurate in space and time while globally and locally conservative.
- Multiphysics: Coupling with external software to solve multiphysics analysis.
- High Fidelity Solver for Flow and Heat Transfer
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- Navier-Stokes equations for incompressible and subsonic compressible flows.
- Stokes model for creeping flow where the viscosity of the fluid is high.
- Convective heat transfer due to the motion of molecules within a fluid, including forced convection and natural convection solved with the Boussinesq density model.
- Conjugate heat transfer analysis in both solids and fluid media.
- Thermal shell feature defined as material medium to simulate heat transfer in thin solid media.
- Viscous and compression heating in case of highly viscous flows and variable density flows.
- A full set of material models for investigating Newtonian and non-Newtonian flow fields.
- Single phase nucleate boiling model to predict local changes in heat flux due to boiling by employing Chen’s correlation.
- Multi-species transport equations to track multiple species in a fluid flow.
- Rich Choices of Turbulence Models for Turbulent Flow Analysis
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- One and two-equation Reynolds Averaged Navier-Stokes (RANS) models for industry applications.
- One and two-equation transition models for solving transition phenomena between laminar flow and turbulent flow.
- Smagorinsky and dynamic sub-grid scale Large Eddy Simulation (LES) models to accurately predict transient turbulence flow.
- Hybrid RANS/LES models as a choice between fast RANS models and expensive but accurate LES.
- Radiation Heat Transfer Modeling
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- Surface to surface radiation heat transfer using gray body enclosure radiation model with distributed memory parallel view-factor computation.
- P1 radiation model to model incident radiation in a gray, optically thick participating medium.
- Discrete ordinates radiation model for modeling radiation heat transfer across semi-transparent media using radiation interfaces.
- Ideal gray surface solar radiation model support to calculate solar heat fluxes using a ray tracing algorithm.
- Multiphase Flow Analysis
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- Levelset method for interface tracking between two immiscible fluids.
- Algebraic Eulerian (Mixture) model for modeling inter-penetrating and dispersed fields.
- Humidity modeling to specify and quantify condensation and evaporation on surfaces in terms of humidity film thickness.
- Multiphase nucleate boiling to predict the onset of nucleate boiling, prompting the air bubble generation at the nucleation site.
- Multiphysics Capabilities
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- Rigid body dynamics coupling.
- Direct-Coupling with Altair OptiStruct to run in a fully-coupled manner for nonlinear fluid/structure interaction analysis using Altair's own proprietary code-coupling interface (CCI) library.
- Direct-Coupling with Altair MotionSolve for multi-body dynamics coupling.
- One-way coupling using acuOptiStruct for thermal stress analysis.
- One-way coupling with Altair OptiStruct to compute the small structural deformation.
- One-way coupling with Altair Flux for electromagnetic thermal-flow interactions.
- One-way coupling with Altair EDEM for particle interactions.
- Moving Mesh Technology
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- Specified or interpolated mesh approaches for simple mesh motion.
- Arbitrary Lagrangian Eulerian (ALE) algorithm for complex deforming mesh motions.
- Flexible body mesh movement.
- Free surface simulation.
- Guide surface technology.
- Sliding/non-conformal mesh technology.
- Optimization
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- Parametric and shape optimization studies completely with AcuSolve.
- Optimization of general objectives and constraints.
- Geometric constraints.
- 3D shapes tool to generate mesh free morph shapes – spline technology.
- Integration with HyperMorph for shape optimization studies.
- 3D printing export capabilities.
- Perform design exploration studies by coupling with HyperStudy.
- Particle Tracing
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- Spherical finite mass and massless particle tracing available as a post-processing or co-processing step.
- Works with steady and unsteady flows, fixed or moving meshes.
- Enhanced Boundary Conditions
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- Atmospheric boundary layer inlet profile support for atmospheric external flow.
- Surface gravity wave inlet support for offshore applications.
- Automatic wall treatment to simplify the CFD set-up workflow for complex industry models.
- Automatic turbulence input parameter calculation based on the turbulence flow types.
- Synthetic turbulence feature for atmospheric external flow.
- Automatic turbulent Prandtl number calculation based on local flow and material properties.
- Component Technology
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- Simplified fan component model.
- Simplified heat exchanger model.
- Porous media support.
- Fast Computing Time using GPU Acceleration
- Altair AcuSolve is supported on CUDA-enabled graphical processing units for even faster performance.
- Powerful User-Defined Function (UDF) Capability
-
- Allows definition of custom material models, source terms, boundary conditions, mesh motion, etc.
- Client-server interface with external programs.
For more information, reference the AcuSolve help manual.
Altair Feko + WinProp
Feko + WinProp is a comprehensive computational electromagnetics (CEM) code used widely in the telecommunications, automobile, space and defense industries. Feko + WinProp offers several frequency and time domain EM solvers. Hybridization of these methods enables the efficient analysis of a broad spectrum of EM problems, including antennas, microstrip circuits, RF components and biomedical systems, the placement of antennas on electrically large structures, the calculation of scattering as well as the investigation of electromagnetic compatibility (EMC).
Feko + WinProp also offers tools that are tailored to solve more challenging EM interactions, including dedicated solvers for characteristic mode analysis (CMA) and bi-directional cables coupling. Special formulations are also included for efficient simulation of integrated windscreen antennas and antenna arrays.
Combined with the MLFMM, and the true hybridization of the solvers, Feko + WinProp is considered the global market leader for antenna placement analysis.
- Benefits
-
- Multiple solvers for users to choose the best method for the problem they are trying to solve
- Industry leading hybridization of different methods when solving complex and electrically large problems
- Excellent performance and reliable accuracy founded on extensive validation of the solver’s numerical methods.
- Specialized solutions, such as characteristic mode analysis (CMA), bidirectional cable coupling, windscreen antennas and large finite arrays
- Model decomposition workflows for classical antenna placement and EMC problems
For more information, reference the Feko + WinProp help manual.
Altair Flux
Flux is the leading software for electromagnetic and thermal simulations. For more than 30 years, Flux simulation software has been used worldwide in the industry and university labs. It has become a reference for the high accuracy it delivers. It is a versatile, efficient and user-friendly tool that will help to generate optimized and high-performance products, in less time and with fewer prototypes. Flux can be used to simulate rotating electromotors, linear actuators and solenoids, transformers, induction heating processes, sensors, cables, and their electric connections. The electromagnetic compatibility of components can also be evaluated.
- Benefits
-
- Accurate results in a very short time for thousands of design configurations
- Fully customizable user preferences and automation with embedded scripting tools
- Parameters for geometric dimensions or physical characteristics enable design exploration
- Different levels of interaction ranging from reduced model extraction to full co-simulation
- Coupling and co-simulation with systems analysis tools and 3D simulation software to generate most realistic analysis results
For more information, reference the Flux help manual.
Altair FluxMotor
FluxMotor is a flexible simulation software dedicated to the pre-design of electric rotating machines. It enables designers to create their motor, assembling standard or customized parts, add windings and materials to run a selection of tests and compare results. Based on modern technology, this standalone platform offers fast and accurate computations. When necessary, model export to Flux finite element software enables to perform more advanced studies, and connection to Altair HyperStudy to achieve effective design exploration and optimization early in the concept phase.
- Benefits
-
- Efficient dedicated environment for e-Motor design, fully customizable
- Rapidity of design and quick computation of performance mapping
- Effective projects management with catalogs, offering instant comparison matrix
- Full model export to Flux 2D/skew/3D to take into account more complex phenomenon (eccentricity, demagnetization, etc.)
- Coupling to HyperStudy to run early optimization from early design stages (combinations, duty cycle performance, etc.)
For more information, reference the FluxMotor help manual.
Altair nanoFluidX
nanoFluidX is a state-of-the-art particle-based (SPH) fluid dynamics code for simulation of single and multiphase flows in complex geometries with complex motion. It can be used to predict the oiling in powertrain systems with rotating shafts/gears and analyze forces and torques on individual components of the system. The software is created and optimized for use on clusters of Graphical Processing Units (GPUs), making it extremely fast. For typical gear-train applications, the code can run an order of magnitude faster than a Finite-Volume code while also including less geometry simplifications.
- Benefits
-
- Accuracy: Particle-based (SPH) fluid dynamics simulation providing highly accurate results
- Turn-Around-Time: Superior solver performance and trivial pre-processing lead to rapid turn-around time
- Multiphase: Air entrapment and windage effects
- Solution-Focused: Drivetrain applications such as gearboxes, differentials, e-motors and crankcase oiling with or without heat transfer.
- Multiphysics: Altair AcuSolve coupling provides steady-state thermal fields on solid components
- Cost: Unique HyperWorks Units licensing system
For more information, reference the nanoFluidX help manual.
Altair ultraFluidX
ultraFluidX is a simulation tool for ultra-fast prediction of the aerodynamic properties of passenger and heavy-duty vehicles, as well as for building, environmental, and motorsport applications. Its cutting-edge technology is optimized for GPUs to deliver unbeatable performance and to allow for overnight simulations even of complex cases on a single server. Conventional simulation approaches need a significant amount of CPU cores to achieve similar turnaround times. ultraFluidX increases throughput, while reducing hardware and energy cost and at the same time delivering the high fidelity of a transient LES simulation.
- Benefits
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- High fidelity: Wall-modeled LES (Large Eddy Simulations) approach based on the Lattice Boltzmann Method provides accurate transient results
- Flexibility: Fully-automated, robust volume mesh generation is integrated in the solver and enables fast design changes
- Robustness: Minimum pre-processing effort due to low surface mesh requirements
- Fast and easy case setup: Altair Virtual Wind Tunnel integration facilitates trivial model setup for external aerodynamics simulations
- High throughput: Efficient multi-GPU implementation enables transient overnight analyses
For more information, reference the ultraFluidX help manual.
Altair Multiscale Designer
Altair Multiscale Designer is an efficient tool for development and simulation of multiscale material models of continuous, woven, and/or chopped fiber composites, honeycomb cores, reinforced concrete, soil, bones, and various other heterogeneous materials. Applications include multiscale material modeling for design, ultimate failure, statistical-based material allowables, fatigue, fracture, impact, crash, environmental degradation, and multiphysics simulations and provides plugins to commercial FEA solvers OptiStruct, Radioss, LS-DYNA, and Abaqus.
For more information, reference the Multiscale Designer help manual.
Altair Seam
Altair Seam is used to predict interior noise and vibration in automobiles, aircraft, and construction equipment cabs as well as the radiated noise from ships and the vibroacoustic environments for spacecraft. Other applications include machinery noise, industrial noise, and building acoustics.