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+
+# Specifying the number of iterations and under-relaxation factors
+
+Abaqus/CFD solves the nonlinear transport equations sequentially for a specified number of iterations. The default is 10000.
+
+# Input File Usage:
+
+Use the following options to specify the number of nonlinear iterations:
+
+\*CFD, INCOMPRESSIBLE NAVIER STOKES, STEADY STATE number of nonlinear iterations
+
+The under-relaxation factors are specified as the last data on the first data line of the corresponding linear equation solvers. Use the following options to specify the under-relaxation factors:
+
+\*MOMENTUM EQUATION SOLVER  
+data for all linear convergence criteria, under-relaxation factor   
+\*TRANSPORT EQUATION SOLVER   
+data for all linear convergence criteria, under-relaxation factor   
+\*PRESSURE EQUATION SOLVER   
+data for all linear convergence criteria, under-relaxation factor   
+\*ENERGY EQUATION SOLVER   
+data for all linear convergence criteria, under-relaxation factor
+
+# Monitoring output variables
+
+Abaqus/CFD provides a number of output variables that are useful for monitoring the health of a calculation and are good indicators for situations where the flow has reached a steady-state condition. These variables are written to the status (.sta) file and can be examined as the analysis job is executing. The RMS divergence output variable is useful for determining if a calculation is proceeding normally. Values of the RMS divergence output variable that are O(1) can indicate that the problem is incorrectly specified or that the calculation has become unstable. The global kinetic energy (KE) provides a good indicator for when the flow has reached a steady state; i.e., when the kinetic energy asymptotically approaches a constant value, the flow is typically achieving a steady-state condition where the velocities and pressure do not vary in time. Alternatively, the global kinetic energy can indicate a steady periodic or chaotic flow situation as well.
+
+# Initial conditions
+
+Initial conditions for the density, velocity, temperature, turbulent eddy viscosity, turbulent kinetic energy, and dissipation rate can be specified (see “Initial conditions in Abaqus/CFD,” Section 34.2.2). If the density is omitted, the specified material density is used for incompressible flow simulations.
+
+For a well-posed incompressible flow problem, the initial velocity must satisfy the boundary conditions and the imposed divergence-free condition; i.e., the solvability conditions. Abaqus/CFD automatically uses the user-defined boundary conditions and tests the specified velocity initial conditions to be sure the solvability conditions are satisfied. If they are not, the initial velocity is projected onto a divergence-free subspace, yielding initial conditions that define a well-posed incompressible
+
+<!-- source-page: 412 -->
+
+Navier-Stokes problem. Therefore, in some circumstances, user-specified velocity initial conditions may be overridden with velocity conditions that satisfy solvability.
+
+# Boundary conditions
+
+Boundary conditions for velocity, temperature, pressure, and eddy viscosity can be defined (see “Boundary conditions in Abaqus/CFD,” Section 34.3.2). During the analysis prescribed boundary conditions can be varied using an amplitude definition (see “Amplitude curves,” Section 34.1.2). All amplitude definitions except smooth step and solution-dependent amplitudes are available. By default, all boundary conditions are applied instantaneously. Velocity and pressure boundary conditions can be specified via user subroutines (see “SMACfdUserPressureBC,” Section 1.3.1 of the Abaqus User Subroutines Reference Guide, and “SMACfdUserVelocityBC,” Section 1.3.2 of the Abaqus User Subroutines Reference Guide).
+
+Displacement and velocity boundary conditions at FSI interfaces are prescribed automatically by the definition of a co-simulation region; therefore, you should not prescribe these conditions at an FSI interface. Similarly, you should not define the temperature at a CHT interface; the temperature is prescribed automatically by the definition of a co-simulation region. For more information, see “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1.
+
+The specification of no-slip/no-penetration boundary conditions at walls requires the specification of the turbulent eddy viscosity and normal-distance function, which is handled automatically by Abaqus/CAE.
+
+# Hydrostatic pressure condition
+
+In incompressible flows, the pressure is known only within an arbitrary additive constant value or the hydrostatic pressure. In many practical situations, the pressure at an outflow boundary may be prescribed, which, in effect, sets the hydrostatic pressure level. In cases where there is no pressure prescribed, it is necessary to set the hydrostatic pressure level at a minimum of one node in the mesh.
+
+The fluid reference pressure can be used to specify the hydrostatic pressure level. When there are no prescribed pressure boundary conditions, the fluid reference pressure establishes the hydrostatic pressure level and makes the pressure-increment equation non-singular. If pressure boundary conditions are prescribed in addition to the reference pressure level, the reference pressure simply adjusts the output pressures according to the specified pressure level. For more information, see “Specifying a fluid reference pressure” in “Concentrated loads,” Section 34.4.2.
+
+# Loads
+
+The loading types for Abaqus/CFD include applied heat flux, volumetric heat-generation sources, general body forces, and gravity loading. Gravity loading defines the gravity vector used with a Boussinesq-type body force in buoyancy driven flow (see “Specifying gravity loading” in “Distributed loads,” Section 34.4.3). Gravity loading can be used only in conjunction with the energy equation and is ignored if used without the energy equation. During the analysis prescribed loads can be varied using an amplitude definition (see “Amplitude curves,” Section 34.1.2). All amplitude definitions except smooth step and solution-dependent amplitudes are available.
+
+<!-- source-page: 413 -->
+
+# Material options
+
+Material definitions in Abaqus/CFD follow the Abaqus conventions but also present several material properties specific to fluid dynamics. In Abaqus/CFD the typical material properties include viscosity, constant-pressure specific heat, density, and coefficient of thermal expansion. The thermal expansion is used with a Boussinesq-type body force in buoyancy driven flow.
+
+In contrast to Abaqus/Standard and Abaqus/Explicit, which use the constant-volume specific heat, the constant-pressure specific heat is required when the energy equation is used for thermal-flow problems. For problems involving an ideal gas, you can optionally specify constant-volume specific heat and the ideal gas constant.
+
+# Elements
+
+Abaqus/CFD supports the following element types: the 8-node hexahedral element, FC3D8; the 6-node triangular prism element, FC3D6; the 5-node pyramid element, FC3D5; and the 4-node tetrahedral element, FC3D4 (see “Fluid (continuum) elements,” Section 28.2.1).
+
+# Output
+
+The output available from Abaqus/CFD for an incompressible fluid dynamic analysis includes both nodal and surface field data and element and surface time-history data. For the nodal and element output, the preselected field and history data include velocity (V), temperature (TEMP), pressure (PRESSURE), and turbulent eddy viscosity (TURBNU). In addition, preselected field data include displacement (U). Preselected data are not available for surface output.
+
+In addition to the preselected output, you can request several derived and auxiliary variables. All of the output variable identifiers are outlined in “Abaqus/CFD output variable identifiers,” Section 4.2.3.
+
+Input file template   
+```txt
+*HEADING
+...
+*NODE
+...
+*ELEMENT, TYPE=FC3D4
+...
+*MATERIAL, NAME=matname
+*CONDUCTIVITY
+Data lines to define the thermal conductivity
+*DENSITY
+Data lines to define the fluid density
+*SPECIFIC HEAT, TYPE=CONSTANT PRESSURE
+Data lines to define the specific heat
+*VISCOSITY 
+```
+
+<!-- source-page: 414 -->
+
+Data lines to define the fluid viscosity   
+*INITIAL CONDITIONS, TYPE=TEMPERATURE, ELEMENT AVERAGE
+Data lines to prescribe initial temperatures at the elements
+*INITIAL CONDITIONS, TYPE=VELX, ELEMENT AVERAGE
+Data lines to prescribe initial x-velocity at the elements
+*INITIAL CONDITIONS, TYPE=VELY, ELEMENT AVERAGE
+Data lines to prescribe initial y-velocity at the elements
+*INITIAL CONDITIONS, TYPE=VELY, ELEMENT AVERAGE
+Data lines to prescribe initial y-velocity at the elements
+...
+*AMPLITUDE, NAME=velxamp, DEFINITION=TABULAR
+Data lines to define amplitude curve to be used for inlet x-velocity
+**
+*STEP
+** Incompressible flow example
+*CFD, INCOMPRESSIBLE NAVIER STOKES, INCREMENTATION=FIXED CFL
+Data lines to define incrementation
+**
+** Boundary conditions
+**
+*FLUID BOUNDARY, TYPE=SURFACE
+inlet_surface, VELX, value for x-velocity
+inlet_surface, VELY, value for y-velocity
+inlet_surface, VELZ, value for z-velocity
+**
+*FLUID BOUNDARY, TYPE=SURFACE
+temperature_surface, TEMP, value for temperature
+**
+*FLUID BOUNDARY, TYPE=SURFACE
+outlet_surface, P, value for pressure
+**
+** Field output
+**
+*OUTPUT, FIELD, TIME INTERVAL=interval for field output
+*ELEMENT OUTPUT
+PRESSURE, TEMP, TURBNU, V
+*NODE OUTPUT
+PRESSURE, TEMP, TURBNU, V
+**
+** History output
+**
+*OUTPUT, HISTORY, FREQUENCY=interval for history output
+
+<!-- source-page: 415 -->
+
+·   
+\*END STEP   
+\*ELEMENT OUTPUT, ELSET=element set for history output, FREQUENCY=SURFACE
+
+# Additional references
+
+• Albets-Chico, X., C. D. Perez-Segarra, A. Olivia, and J. Bredberg, “Analysis of Wall-Function Approaches using Two-Equation Turbulence Models,” International Journal of Heat and Mass Transfer, vol. 51, p. 4940–4957, 2008.   
+• Casey, M., and T. Wintergerste, ERCOFTAC Special Interest Group on “Quality and Trust in Industrial CFD”, European Research Community on Flow, Turbulence and Combustion (ERCOFTAC), 2000.   
+• Chen, H. C., and V. C. Patel, “Near-Wall Turbulence Models for Complex Flows Including Separation,” AIAA Journal, vol. 26, no. 6, p. 641–648, 1988.   
+• Craft, T. J., A. V. Gerasimov, H. Iacovides, and B. E. Launder, “Progress in the Generalization of Wall-Function Treatments,” International Journal of Heat and Fluid Flow, vol. 23, p. 148–160, 2002.   
+• Durbin, P. A., “Limiters and wall treatments in applied turbulence modeling,” Fluid Dynamics research, vol. 41, p. 1–17, 2009.   
+• Jayatilleke, C. L., “The Influence of Prandtl Number and Surface Roughness on the Resistance of the Laminar Sub-Layer to Momentum and Heat Transfer,” Progress in Heat and Mass Transfer, vol. 1, p. 193–330, 1969.   
+• Jongen, T., “Simulation and Modeling of Turbulent Incompressible Flows,” Ph.D. Thesis Lausanne EPFL, 1998.   
+• Kader, B., “Temperature and Concentration Profiles in Fully Turbulent Boundary Layers,” International Journal of Heat and Mass Transfer, vol. 24, no. 9, p. 1541–1544, 1981.   
+• Launder, B. E., and D. B. Spalding, “The Numerical Computation of Turbulent Flows,” Computer Methods in Applied Mechanics and Engineering, vol. 3, p. 269–289, 1974.   
+• Menter, F. R., “Influence of Freestream Values on k– Turbulence Model Predictions,” AIAA Journal, vol. 30, no. 6, p. 1657–1659, 1992.   
+• Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Application,” AIAA Journal, vol. 32, no. 8, p. 1598–1605, 1994.   
+• Nield, D.A., and A. Bejan, Convection in Porous Media, Springer, New York, Third edition, 2010.   
+• Reichardt, H., “Vollstandige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Leitungen,” Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), vol. 31, p. 208–219, 1951.   
+• Shih, T. H., W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, “A New k– Eddy Viscosity Model for High Reynolds Number Turbulent Flows,” Computers and Fluids, vol. 24, no. 3, p. 227–238, 1995.
+
+<!-- source-page: 416 -->
+
+• Wilcox, D. C., “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models,” AIAA Journal, vol. 26, no. 11, p. 1299–1310, 1988.   
+• Yakhot, V., S. A. Orszag, S. Thangam, T. B. Gatski, and C. G. Speziale, “Development of Turbulence Models for Shear Flows by a Double Expansion Technique,” Physics of Fluids A, vol. 4, no. 7, p. 1510–1520, 1992.
+
+<!-- source-page: 417 -->
+
+# 6.7 Electromagnetic analysis
+
+• “Electromagnetic analysis procedures,” Section 6.7.1   
+• “Piezoelectric analysis,” Section 6.7.2   
+• “Coupled thermal-electrical analysis,” Section 6.7.3   
+• “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4   
+• “Eddy current analysis,” Section 6.7.5   
+• “Magnetostatic analysis,” Section 6.7.6
+
+<!-- source-page: 418 -->
+
+<!-- source-page: 419 -->
+
+# 6.7.1 ELECTROMAGNETIC ANALYSIS PROCEDURES
+
+# Overview
+
+Abaqus/Standard offers several analysis procedures to model piezoelectric, electrical conduction, and electromagnetic phenomena. The distinct electrical phenomena modeled by these procedures is described first, followed by a brief overview of each procedure.
+
+# Electrostatic, electrical conduction, magnetostatic, and electromagnetic analyses
+
+Piezoelectric effect is the electromechanical interaction exhibited by some materials. This coupled electrostatic-structural response is modeled using piezoelectric analysis in Abaqus/Standard. In this procedure the electric potential is a degree of freedom and its conjugate is the electric charge.
+
+Coupled thermal-electrical conduction, with or without structural coupling, is modeled using electrical procedures. In these procedures the electric potential is a degree of freedom and its conjugate is the electric current. While transient effects are ignored in electrical conduction, thus making it steady state, thermal fields can be modeled either as transient or steady state.
+
+Magnetostatic analysis is used to compute the magnetic fields due to direct currents. It solves the magnetostatic approximation to Maxwell’s equations. The magnetic vector potential is a degree of freedom in a magnetostatic analysis, and its conjugate is the surface current.
+
+Electromagnetic analysis is used to model the full coupling between time-varying electric and magnetic fields by solving Maxwell’s equations. In such an analysis the magnetic vector potential is a degree of freedom and its conjugate is the surface current.
+
+# Electrostatic procedure
+
+The following electrostatic analysis procedure is available in Abaqus/Standard:
+
+• Piezoelectric analysis: In a piezoelectric material an electric potential gradient causes straining, while stress causes an electric potential in the material (“Piezoelectric analysis,” Section 6.7.2). This coupling is provided by defining the piezoelectric and dielectric coefficients of a material and can be used in natural frequency extraction, transient dynamic analysis, both linear and nonlinear static stress analysis, and steady-state dynamic analysis procedures. In all procedures, including nonlinear statics and dynamics, the piezoelectric behavior is always assumed to be linear.
+
+# Steady electrical conduction procedures
+
+The following electrical conduction analyses procedures are available in Abaqus/Standard:
+
+• Coupled thermal-electrical analysis: The electric potential and temperature fields can be solved simultaneously by performing a coupled thermal-electrical analysis (“Coupled thermal-electrical analysis,” Section 6.7.3). In these problems the energy dissipated by an electrical current flowing through a conductor is converted into thermal energy, and the electrical conductivity can, in turn, be temperature dependent. Thermal loads can be applied, but deformation of the structure is not considered. Coupled thermal-electrical problems can be linear or nonlinear.
+
+<!-- source-page: 420 -->
+
+• Fully coupled thermal-electrical-structural analysis: A coupled thermal-electrical-structural analysis is used to solve simultaneously for the stress/displacement, the electric potential, and the temperature fields. A coupled analysis is used when the thermal, electrical, and mechanical solutions affect each other strongly. An example of such a process is resistance spot welding, where two or more metal parts are joined by fusion at discrete points at the material interface. The fusion is caused by heat generated due to the current flow at the contact points, which depends on the pressure applied at these points.
+
+These problems can be transient or steady state and linear or nonlinear. Cavity radiation effects cannot be included in a fully coupled thermal-electrical-structural analysis. See “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4, for more details.
+
+# Magnetostatic procedure
+
+The following magnetostatic analysis procedure is available in Abaqus/Standard:
+
+• Magnetostatic analysis: A magnetostatic analysis is used to solve for the magnetic vector potential, from which the magnetic field is computed in the entire domain. For example, the magnetic field due to the flow of direct current can be modeled. The procedure supports linear as well as nonlinear magnetic material properties. See “Magnetostatic analysis,” Section 6.7.6, for more details.
+
+# Electromagnetic procedures
+
+Electromagnetic analyses are used to solve for the magnetic vector potential, from which both electric and magnetic fields are computed in the entire domain. The following electromagnetic analysis procedures are available in Abaqus/Standard:
+
+• Time-harmonic eddy current analysis: This procedure assumes time-harmonic excitation and response. It supports linear electrical conductivity and linear magnetic material behavior. For example, eddy currents induced in a workpiece that is in the vicinity of a source of excitation (such as a coil carrying alternating current) can be modeled. See “Time-harmonic analysis” in “Eddy current analysis,” Section 6.7.5, for more details.
+
+• Transient eddy current analysis: This procedure assumes general time variation of the excitation and response. It supports linear electrical conductivity and both linear and nonlinear magnetic material behavior. For example, eddy currents induced in a workpiece that is in the vicinity of a source of excitation (such as a coil carrying time-varying current) can be modeled. See “Transient analysis” in “Eddy current analysis,” Section 6.7.5, for more details.