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Flux limiter

Flux limiters are used in high resolution schemes – numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations (PDEs)

Weakened weak form

Weakened weak form (or W2 form) is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings. These numerical methods are applicable to solid

MOOSE (software)

MOOSE (Multiphysics Object Oriented Simulation Environment) is an object-oriented C++ finite element framework for the development of tightly coupled multiphysics solvers from Idaho National Laborator

WAMIT

WAMIT is a computer program for computing wave loads and motions of offshore structures in waves. It is based on the linear and second-order potential theory. The velocity potential is solved by means

Computational fluid dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform

Numerical methods in fluid mechanics

Fluid motion is governed by the Navier–Stokes equations, a set of coupled and nonlinearpartial differential equations derived from the basic laws of conservation of mass, momentumand energy. The unkno

CGNS

CGNS stands for CFD General Notation System. It is a general, portable, and extensible standard for the storage and retrieval of CFD analysis data. It consists of a collection of conventions, and free

Detached eddy simulation

Detached eddy simulation (DES) is a modification of a Reynolds-averaged Navier–Stokes equations (RANS) model in which the model switches to a subgrid scale formulation in regions fine enough for large

Avizo (software)

Avizo (pronounce: ‘a-VEE-zo’) is a general-purpose commercial software application for scientific and industrial data visualization and analysis. Avizo is developed by Thermo Fisher Scientific and was

Spectral element method

In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high degree piecewi

AUSM

AUSM stands for Advection Upstream Splitting Method. It is developed as a numerical inviscid flux function for solving a general system of conservation equations. It is based on the upwind concept and

High-resolution scheme

High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following prope

Hemodynamics

Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control sys

Lagrangian and Eulerian specification of the flow field

In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time

Total variation diminishing

In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this me

Calculation of buoyancy flows and flows inside buildings

Buoyancy force is the defined as the force exerted on the body or an object when inserted in a fluid. Buoyancy force is based on the basic principle of pressure variation with depth, since pressure in

MUSCL scheme

In the study of partial differential equations, the MUSCL scheme is a finite volume method that can provide highly accurate numerical solutions for a given system, even in cases where the solutions ex

Kameleon FireEx KFX

Kameleon FireEx KFX, often only referred to as KFX, is a commercial Computational Fluid Dynamics (CFD) program with main focus on gas dispersion and fire simulation. KFX uses the k-epsilon model for t

Upwind scheme

In computational physics, the term upwind scheme (sometimes advection scheme) typically refers to a class of numerical discretization methods for solving hyperbolic partial differential equations, in

Mesh generation

Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells.Often these cells form a simplicial complex.Usually the

Overflow (software)

OVERFLOW - the grid FLOW solver - is a software package for simulating fluid flow around solid bodies using computational fluid dynamics (CFD). It is a compressible 3-D flow solver that solves the tim

Meshfree methods

In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with

Lambda2 method

The Lambda2 method, or Lambda2 vortex criterion, is a vortex core line detection algorithm that can adequately identify vortices from a three-dimensional fluid velocity field. The Lambda2 method is Ga

Finite volume method for three-dimensional diffusion problem

Finite volume method (FVM) is a numerical method. FVM in computational fluid dynamics is used to solve the partial differential equation which arises from the physical conservation law by using discre

Finite volume method for unsteady flow

Unsteady flows are characterized as flows in which the properties of the fluid are time dependent. It gets reflected in the governing equations as the time derivative of the properties are absent.For

Advanced Simulation Library

Advanced Simulation Library (ASL) is free and open-source hardware-accelerated multiphysics simulation platform. It enables users to write customized numerical solvers in C++ and deploy them on a vari

Navier–Stokes equations

In physics, the Navier–Stokes equations (/nævˈjeɪ stoʊks/ nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and phys

Sod shock tube

The Sod shock tube problem, named after Gary A. Sod, is a common test for the accuracy of computational fluid codes, like Riemann solvers, and was heavily investigated by Sod in 1978.The test consists

SIMPLE algorithm

In computational fluid dynamics (CFD), the SIMPLE algorithm is a widely used numerical procedure to solve the Navier–Stokes equations. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked

Central differencing scheme

In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and pro

Flow Science, Inc.

Flow Science, Inc. is a developer of software for computational fluid dynamics, also known as CFD, a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems

Boundary conditions in computational fluid dynamics

Almost every computational fluid dynamics problem is defined under the limits of initial and boundary conditions. When constructing a staggered grid, it is common to implement boundary conditions by a

Combustion models for CFD

Combustion models for CFD refers to combustion models for computational fluid dynamics. Combustion is defined as a chemical reaction in which a hydrocarbon fuel reacts with an oxidant to form products

Aeroacoustic analogy

Acoustic analogies are applied mostly in numerical aeroacoustics to reduce aeroacoustic sound sources to simple emitter types. They are therefore often also referred to as aeroacoustic analogies. In g

Dissipative particle dynamics

Dissipative particle dynamics (DPD) is an off-lattice mesoscopic simulation technique which involves a set of particles moving in continuous space and discrete time. Particles represent whole molecule

Turbulence kinetic energy

In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by meas

Lattice gas automaton

Lattice gas automata (LGCA), or lattice gas cellular automata, are a type of cellular automaton used to simulate fluid flows, pioneered by Hardy–Pomeau–de Pazzis and Frisch–Hasslacher–Pomeau. They wer

Vorticity confinement

Vorticity confinement (VC), a physics-based computational fluid dynamics model analogous to shock capturing methods, was invented by Dr. John Steinhoff, professor at the University of Tennessee Space

WENO methods

In numerical solution of differential equations, WENO (weighted essentially non-oscillatory) methods are classes of high-resolution schemes. WENO are used in the numerical solution of hyperbolic parti

Scarborough criterion

The Scarborough criterion is used for satisfying convergence of a solution while solving linear equations using an iterative method.

CTAG

CTAG is a computational fluid dynamics model for the behaviour of air pollutants on and near roadways. CTAG stands for Comprehensive Turbulent Aerosol Dynamics and Gas Chemistry, is an environmental t

RELAP5-3D

RELAP5-3D is a simulation tool that allows users to model the coupled behavior of the reactor coolant system and the core for various operational transients and postulated accidents that might occur i

Riemann problem

A Riemann problem, named after Bernhard Riemann, is a specific initial value problem composed of a conservation equation together with piecewise constant initial data which has a single discontinuity

TELEMAC

In computational fluid dynamics, TELEMAC is short for the open TELEMAC-MASCARET system, or a suite of finite element computer program owned by the Laboratoire National d'Hydraulique et Environnement (

Immersed boundary method

In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coup

CFD in buildings

CFD stands for computational fluid dynamics (and heat transfer). As per this technique, the governing differential equations of a flow system or thermal system are known in the form of Navier–Stokes e

Lax–Wendroff method

The Lax–Wendroff method, named after Peter Lax and Burton Wendroff, is a numerical method for the solution of hyperbolic partial differential equations, based on finite differences. It is second-order

Simple chemical reacting system

The simple chemical reacting system (SCRS) is one of the combustion models for computational fluid dynamics. This model helps us to determine the process of combustion which is a vital phenomenon used

QUICK scheme

In computational fluid dynamics QUICK, which stands for Quadratic Upstream Interpolation for Convective Kinematics, is a higher-order differencing scheme that considers a three-point upstream weighted

Unified methods for Computing Incompressible and Compressible flow

Computation of Incompressible and Compressible flow generally depends on the Mach Number M, where for a range of zero to supersonic compressible equations are applied but with a possible error on a ra

Code Saturne

code_saturne is a general-purpose computational fluid dynamics free computer software package. Developed since 1997 at Électricité de France R&D, code_saturne is distributed under the GNU GPL licence.

Nonequilibrium Gas and Plasma Dynamics Laboratory

The Nonequilibrium Gas and Plasma Dynamics Laboratory (NGPDL) at the Aerospace Engineering Department of the University of Colorado Boulder is headed by Professor Iain D. Boyd and performs research of

Taylor–Green vortex

In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates. It

Tecplot

Tecplot is the name of a family of visualization & analysis software tools developed by American company Tecplot, Inc., which is headquartered in Bellevue, Washington. The firm was formerly operated a

Coolfluid

COOLFluiD is a component based scientific computing environment that handles high-performance computing problems with focus on complex computational fluid dynamics (CFD) involving multiphysics phenome

Computational aeroacoustics

Computational aeroacoustics is a branch of aeroacoustics that aims to analyze the generation of noise by turbulent flows through numerical methods.

ENO methods

ENO (essentially non-oscillatory) methods are classes of high-resolution schemes in numerical solution of differential equations.

Reynolds-averaged Navier–Stokes equations

The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averagedequations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous qu

Lax–Wendroff theorem

In computational mathematics, the Lax–Wendroff theorem, named after Peter Lax and Burton Wendroff, states that if a conservative numerical scheme for a hyperbolic system of conservation laws converges

Generalized Environmental Modeling System for Surfacewaters

Generalized Environmental Modeling System for Surfacewaters or GEMSS is a public domain software application published by ERM. It has been used for hydrological studies throughout the world.

ADINA

ADINA is a commercial engineering simulation software program that is developed and distributed worldwide by ADINA R & D, Inc. The company was founded in 1986 by Dr. Klaus-Jürgen Bathe, and is headqua

Pencil Code

The Pencil Code is a high-order finite-difference code for solving partial differential equations, written in Fortran 95. The code is designed for efficient computation with massive parallelization. D

Grid classification

Grid or mesh is defined as smaller shapes formed after discretisation of geometric domain. Mesh or grid can be in 3- dimension and 2-dimension. Meshing has applications in the fields of geography, des

Flux-corrected transport

Flux-corrected transport (FCT) is a conservative shock-capturing scheme for solving Euler equations and other hyperbolic equations which occur in gas dynamics, aerodynamics, and magnetohydrodynamics.

Iterative Stencil Loops

Iterative Stencil Loops (ISLs) are a class of numerical data processing solutionwhich update array elements according to some fixed pattern, called a stencil. They are most commonly found in computer

Spatial twist continuum

In finite element analysis, the spatial twist continuum (STC) is a dual representation of a hexahedral mesh that defines the global connectivity constraint. Generation of an STC can simplify the autom

Computational methods for free surface flow

In physics, a free surface flow is the surface of a fluid flowing that is subjected to both zero perpendicular normal stress and parallel shear stress. This can be the boundary between two homogeneous

Cavitation modelling

Cavitation modelling is a type of computational fluid dynamic (CFD) that represents the flow of fluid during cavitation. It covers a wide range of applications, such as pumps, water turbines, pump ind

Explicit algebraic stress model

The algebraic stress model arises in computational fluid dynamics. Two main approaches can be undertaken. In the first, the transport of the turbulent stresses is assumed proportional to the turbulent

Volume of fluid method

In computational fluid dynamics, the volume of fluid (VOF) method is a free-surface modelling technique, i.e. a numerical technique for tracking and locating the free surface (or fluid–fluid interface

Computational magnetohydrodynamics

Computational magnetohydrodynamics (CMHD) is a rapidly developing branch of magnetohydrodynamics that uses numerical methods and algorithms to solve and analyze problems that involve electrically cond

Particle-in-cell

In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in

KIVA (software)

KIVA is a family of Fortran-based Computational Fluid Dynamics software developed by Los Alamos National Laboratory (LANL). The software predicts complex fuel and air flows as well as ignition, combus

Material point method

The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization me

PISO algorithm

PISO algorithm (Pressure-Implicit with Splitting of Operators) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the SIMPLE

Diffuse element method

In numerical analysis the diffuse element method (DEM) or simply diffuse approximation is a meshfree method. The diffuse element method was developed by B. Nayroles, G. Touzot and Pierre Villon at the

Courant–Friedrichs–Lewy condition

In mathematics, the convergence condition by Courant–Friedrichs–Lewy is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) numerically

Projection method (fluid dynamics)

In fluid dynamics, The projection method is an effective means of numerically solving time-dependent incompressible fluid-flow problems. It was originally introduced by Alexandre Chorin in 1967as an e

MacCormack method

In computational fluid dynamics, the MacCormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite differen

Marker-and-cell method

The marker-and-cell method is commonly used in computer graphics to discretize functions for fluid and other simulations. It was developed by Francis Harlow and his collaborators at the Los Alamos Nat

ADCIRC

The ADCIRC model is a high-performance, cross-platform numerical ocean circulation model popular in simulating storm surge, tides, and coastal circulation problems.Originally developed by Drs. and ,th

HPP model

The Hardy–Pomeau–Pazzis (HPP) model is a fundamental lattice gas automaton for the simulation of gases and liquids. It was a precursor to the lattice Boltzmann methods. From lattice gas automata, it i

Multiphase particle-in-cell method

The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC met

Godunov's theorem

In numerical analysis and computational fluid dynamics, Godunov's theorem — also known as Godunov's order barrier theorem — is a mathematical theorem important in the development of the theory of high

Lax–Friedrichs method

The Lax–Friedrichs method, named after Peter Lax and Kurt O. Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can

Godunov's scheme

In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by S. K. Godunov in 1959, for solving partial differential equations. One can thi

Natural element method

The natural element method (NEM) is a meshless method to solve partial differential equation, where the elements do not have a predefined shape as in the finite element method, but depend on the geome

FLACS

FLACS (FLame ACceleration Simulator) is a commercial Computational Fluid Dynamics (CFD) software used extensively for explosion modeling and atmospheric dispersion modeling within the field of industr

Power law scheme

The power law scheme was first used by Suhas Patankar (1980). It helps in achieving approximate solutions in computational fluid dynamics (CFD) and it is used for giving a more accurate approximation

Exa Corporation

Exa Corporation was a developer and distributor of computer-aided engineering (CAE) software. Its main product was PowerFLOW, a lattice-boltzmann derived implementation of computational fluid dynamics

Finite volume method for one-dimensional steady state diffusion

The Finite volume method in computational fluid dynamics is a discretization technique for partial differential equations that arise from physical conservation laws. These equations can be different i

Types of mesh

A mesh is a representation of a larger geometric domain by smaller discrete cells. Meshes are commonly used to compute solutions of partial differential equations and render computer graphics, and to

Fluid animation

Fluid animation refers to computer graphics techniques for generating realistic animations of fluids such as water and smoke. Fluid animations are typically focused on emulating the qualitative visual

PLOT3D file format

In computational fluid dynamics, the PLOT3D file format is a standard file format used for storing grid and results data. PLOT3D was created by NASA Ames Research Center in 1982 by Pieter Buning and r

Boundary element method

The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form)

Quadrature based moment methods

Quadrature-based moment methods (QBMM) are a class of computational fluid dynamics (CFD) methods for solving Kinetic theory and is optimal for simulating phases such as rarefied gases or dispersed pha

Shock-capturing method

In computational fluid dynamics, shock-capturing methods are a class of techniques for computing inviscid flows with shock waves. The computation of flow containing shock waves is an extremely difficu

Level-set method

Level-set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level-set model is that one can perform numerical

Beam and Warming scheme

In numerical mathematics, Beam and Warming scheme or Beam–Warming implicit scheme introduced in 1978 by Richard M. Beam and R. F. Warming, is a second order accurate implicit scheme, mainly used for s

Multi-particle collision dynamics

Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD), is a particle-based mesoscale simulation technique for complex fluids which fully incorporates thermal fluctu

Lattice Boltzmann methods

The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is a class of computational fluid dynamics (CFD) m

Gerris (software)

Gerris is computer software in the field of computational fluid dynamics (CFD). Gerris was released as free and open-source software, subject to the requirements of the GNU General Public License (GPL

FEATool Multiphysics

FEATool Multiphysics ("Finite Element Analysis Toolbox for Multiphysics") is a physics, finite element analysis (FEA), and PDE simulation toolbox. FEATool Multiphysics features the ability to model fu

Viscous vortex domains method

The viscous vortex domains (VVD) method is a mesh-free method of computational fluid dynamics for directly numerically solving 2D Navier-Stokes equations in Lagrange coordinates.It doesn't implement a

Finite volume method

The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.In the finite volume method, volume integrals in a partial

Simcenter STAR-CCM+

Simcenter STAR-CCM+ is a commercial Computational Fluid Dynamics (CFD) based simulation software developed by Siemens Digital Industries Software. Simcenter STAR-CCM+ allows the modeling and analysis

Wirth Research

Wirth Research is a group of engineering companies, founded by Nicholas Wirth in 2003, specialising in research, development, design and manufacture for the motor racing industry and other high techno

Particle method

In the field of numerical analysis, particle methods discretize fluid into particles. Particle methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computi

Finite pointset method

In applied mathematics, the name finite pointset method is a general approach for the numerical solution of problems in continuum mechanics, such as the simulation of fluid flows. In this approach (of

Gamma-Re Transition Model

Gamma-Re (γ-Re) transition model is a two equation model used in Computational Fluid Dynamics (CFD) to modify turbulent transport equations to simulate laminar, laminar-to-turbulent and turbulence sta

Finite volume method for two dimensional diffusion problem

The methods used for solving two dimensional Diffusion problems are similar to those used for one dimensional problems. The general equation for steady diffusion can be easily derived from the general

Riemann solver

A Riemann solver is a numerical method used to solve a Riemann problem. They are heavily used in computational fluid dynamics and computational magnetohydrodynamics.

Upwind differencing scheme for convection

The upwind differencing scheme is a method used in numerical methods in computational fluid dynamics for convection–diffusion problems. This scheme is specific for Peclet number greater than 2 or less

SU2 code

SU2 is a suite of open-source software tools written in C++ for the numerical solution of partial differential equations (PDE) and performing PDE-constrained optimization. The primary applications are

False diffusion

False diffusion is a type of error observed when the upwind scheme is used to approximate the convection term in convection–diffusion equations. The more accurate central difference scheme can be used

SIMPLEC algorithm

The SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of SIMPLE algorithm; is a commonly used numerical procedure in Computational Fluid Dynamics to so

FTCS scheme

In numerical analysis, the FTCS (Forward Time Centered Space) method is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations.

OpenLB

OpenLB is an object-oriented implementation of the lattice Boltzmann methods (LBM). It is the first implementation of a generic platform for LBM programming, which is shared with the open source commu

Stochastic Eulerian Lagrangian method

In computational fluid dynamics, the Stochastic Eulerian Lagrangian Method (SELM) is an approach to capture essential features of fluid-structure interactions subject to thermal fluctuations while int

Pumplinx

PumpLinx is a 3-D computational fluid dynamics (CFD) software developed for the analysis of fluid pumps, motors, compressors, valves, propellers, hydraulic systems, and other fluid devices with rotati

High pressure jet

A high pressure jet is a stream of pressurized fluid that is released from an environment at a significantly higher pressure than ambient pressure from a nozzle or orifice, due to operational or accid

Pressure-correction method

Pressure-correction method is a class of methods used in computational fluid dynamics for numerically solving the Navier-Stokes equations normally for incompressible flows.

Large eddy simulation

Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, a

Ansys

Ansys, Inc. is an American company based in Canonsburg, Pennsylvania. It develops and markets CAE/multiphysics engineering simulation software for product design, testing and operation and offers its

Computational Fluid Dynamics for Phase Change Materials

Computational Fluid Dynamics (CFD) modeling and simulation for phase change materials (PCMs) is a technique to analyze the performance and behavior of PCMs. The CFD models have been successful in stud

Smoothed-particle hydrodynamics

Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan

Bhatnagar–Gross–Krook operator

The Bhatnagar–Gross–Krook operator (abbreviated BGK operator) term refers to a collision operator used in the Boltzmann equation and in the lattice Boltzmann method, a computational fluid dynamics tec

Variational multiscale method

The variational multiscale method (VMS) is a technique used for deriving models and numerical methods for multiscale phenomena. The VMS framework has been mainly applied to design stabilized finite el

British Hydromechanics Research Association

The British Hydromechanics Research Association is a former government research association that supplies consulting engineering over fluid dynamics.

CFD-FASTRAN

CFD-FASTRAN is a commercial Computational Fluid Dynamics (CFD) software package developed by ESI Group for aerodynamic and aerothermodynamic applications. It employs multiple moving body capability fo

Application of CFD in thermal power plants

Computational fluid dynamics (CFD) are used to understand complex thermal flow regimes in power plants. The thermal power plant may be divided into different subsectors and the CFD analysis applied to

OpenFOAM

OpenFOAM (for "Open-source Field Operation And Manipulation") is a C++ toolbox for the development of customized numerical solvers, and pre-/post-processing utilities for the solution of continuum mec

Gradient-enhanced kriging

Gradient-enhanced kriging (GEK) is a surrogate modeling technique used in engineering. A surrogate model (alternatively known as a metamodel, response surface or emulator) is a prediction of the outpu

Nektar++

Nektar++ is a spectral/hp element framework designed to support the construction of efficient high-performance scalable solvers for a wide range of partial differential equations (PDE). The code is re

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