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Physics Simulation
Simcenter STAR-CCM+ can model a wide range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. Scenarios with multiple time scales can be solved within the same simulation.
Adjoint
The adjoint method is an efficient means to predict the influence of many design parameters and physical inputs on some engineering quantity of interest, that is, on the engineering objective of the simulation. In other words, it provides the sensitivity of the objective (output) with respect to the design variables (input).
Adjoint Analysis Workflow
An adjoint analysis is performed in two major steps. First, you simulate the steady problem using the coupled flow model, or both the coupled flow and coupled energy models. The result of this simulation is referred to as the "primal solution". The primal solution can involve isothermal fluid flow, fluid flow with energy, conduction in solids, or conjugate heat transfer between fluids and solids. In a following step, you set up and run the adjoint analysis starting from the previously obtained primal solution. Instead of running an adjoint simulation stepwise, Simcenter STAR-CCM+ also provides the methodology to set up a user defined adjoint workflow through Simulation Operations.
Creating the Adjoint Cost Functions
You define at least one cost function before you start the adjoint analysis. You can also create additional cost functions within the same simulation. Each cost function is solved sequentially in the order they appear under the Adjoint Cost Functions node in the simulation tree.

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Physics Simulation
Simcenter STAR-CCM+ can model a wide range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. Scenarios with multiple time scales can be solved within the same simulation.
- Defining Physics Workflow
  Simcenter STAR-CCM+ contains a wide range of physics models and methods for the simulation of single- and multi-phase fluid flow, heat transfer, turbulence, solid stress, dynamic fluid body interaction, aeroacoustics, and related phenomena. These physics models are all selected using a physics continuum.
- Setting Up Physics
  This section provides information on how to set up physics models in STAR-CCM+.
- Running Physics Simulations
  This part of the documentation describes preparation and procedures for running a Simcenter STAR-CCM+ simulation.
- Motion
  In general, motion can be defined as the change in position of a body with respect to a certain reference frame.
- Space
  The primary function of the Space models in Simcenter STAR-CCM+ is to provide methods for computing and accessing mesh metrics. Examples of mesh metrics include cell volume and centroid, face area and centroid, cell and face indexes, and skewness angle.
- Time
  The primary function of the time models in Simcenter STAR-CCM+ is to provide solvers that control the iteration and/or unsteady time-stepping.
- Mesh Motion and Adaption
  Many simulations that involve motion or geometry change require you to move or deform the mesh. Other simulations require localized mesh adaption in order to achieve an accurate solution.
- Materials
  Material models simulate substances, including various mixtures.
- Fluid Flow
  Many engineering design projects require you to predict the effect of flowing fluids on containing structures or immersed objects. While you can analyse simple scenarios with hand calculations, complex scenarios require you to apply numerical methods for accurate solutions.
- Viscous Flow
  Viscous Flow is a finite element approach for use with viscoelastic materials and other highly viscous non-Newtonian fluids, such as liquid plastics and rubber, dough and similar foodstuffs, molten glass, and mud. Viscoelastic materials resemble elastic materials, but also exhibit viscous effects, rebounding slowly from deformations.
- Passive Scalars
  Passive scalars are user-defined variables of arbitrary value, assigned to fluid phases or individual particles. They are passive because they do not affect the physical properties of the simulation. An intuitive way to think of passive scalars is as tracer dye in a fluid, but with numerical values instead of colors, and with no appreciable mass or volume.
- Heat Transfer
  Heat transfer is the study of energy in transit due to a temperature difference in a medium or between media. Heat transfer extends thermodynamic analysis through the study of the modes of energy transfer and through development of relations to calculate energy transfer rates.
- Species
  This chapter provides information about the chemical species models in Simcenter STAR-CCM+. A species model is activated whenever a multi-component liquid or multi-component gas is chosen from the Material model section of the Physics Model Selection dialog.
- Porous Media
  Simcenter STAR-CCM+ allows you to simulate the transport of a fluid or energy (e.g. heat, electrical charge) through porous materials using the concept that the action of the porous media can be represented using appropriate loss (or 'diffusion') coefficients.
- Adjoint
  The adjoint method is an efficient means to predict the influence of many design parameters and physical inputs on some engineering quantity of interest, that is, on the engineering objective of the simulation. In other words, it provides the sensitivity of the objective (output) with respect to the design variables (input).
  - Adjoint Analysis Workflow
    An adjoint analysis is performed in two major steps. First, you simulate the steady problem using the coupled flow model, or both the coupled flow and coupled energy models. The result of this simulation is referred to as the "primal solution". The primal solution can involve isothermal fluid flow, fluid flow with energy, conduction in solids, or conjugate heat transfer between fluids and solids. In a following step, you set up and run the adjoint analysis starting from the previously obtained primal solution. Instead of running an adjoint simulation stepwise, Simcenter STAR-CCM+ also provides the methodology to set up a user defined adjoint workflow through Simulation Operations.
    - Computing the Mesh Sensitivity
      The mesh sensitivity gives the sensitivity of the cost function associated with mesh deformation.
    - Computing the Surface Sensitivity
      The surface sensitivity model allows you to identify which areas of geometry are most critical to the cost functions of interest. The sensitivity field can be further used in computing displacements that are then used to deform the mesh for shape optimization. To reduce computation time compared to the mesh sensitivity, the model computes approximate sensitivities with respect to surface position for the selected adjoint cost functions Surface Sensitivity of [cost function] w.r.t Position.
    - Creating the Adjoint Cost Functions
      You define at least one cost function before you start the adjoint analysis. You can also create additional cost functions within the same simulation. Each cost function is solved sequentially in the order they appear under the Adjoint Cost Functions node in the simulation tree.
    - Defining Adjoint Stopping Criteria
      Aside from the general stopping criteria for the primal and adjoint solvers, you can create individual stopping criteria for each cost function. With this option, you can run various cost functions with different conditions for stopping the adjoint solver. When either global or cost function specific criteria are met, the adjoint solver moves to the solution of the next cost function, or stops completely if there are no more cost functions to solve.
    - Running the Adjoint Solver
      The adjoint solver solves the linear system of equations for the flow and the solid energy adjoint. In a multi-objective optimization, you have the possibility to solve these linear system for one active or one set of active cost functions.
  - Adjoint Shape Optimization
    An adjoint shape optimization uses adjoint sensitivities to derive an optimized shape with respect to the user-defined cost functions. For example, an optimized duct shape reduces the total pressure drop (cost function) in the duct.
  - Adjoint Topology Optimization
    Advances in additive manufacturing technology make it possible to create components whose shape is determined by simulation-based generative engineering. Simcenter STAR-CCM+ provides a topology optimization method that generates flow channels by placing solid material in those parts of the design space that do not contribute to the engineering objective.
  - Enhancing the Coupled Flow Solver Convergence Behavior
    For a standard flow analysis, the residuals of the flow variables are not required to converge to machine precision. However, to ensure that the adjoint solver converges in a robust manner, it is important to obtain a certain level of convergence in the primal solution.
  - Computing Adjoint Error Estimates
    Adjoint Error Estimates highlight locations in the flow where high numerical inaccuracy impacts the accuracy of the respective cost function. You compute Adjoint Error Estimates for specific cost functions, (such as pressure drop in a channel or airfoil drag), after the Adjoint solution is complete. You access Adjoint Error Estimates through field functions.
  - Computing Adjoint Parameter Sensitivities
    Adjoint Parameter Sensitivity allows you to compute the effect of a given global parameter on the cost function (objective) of interest. You can use parameter sensitivities to investigate how your simulation boundary conditions impact your engineering objectives, and potentially optimize these conditions, for any type of adjoint flow analysis.
  - User Source Terms Within Adjoint
    For certain cases where you provide source terms that supplement the flow equations, Simcenter STAR-CCM+ differentiates these source terms provided they are defined using field functions that use supported quantities and operators.
  - Troubleshooting the Adjoint Solver
    Similar to a standard flow simulation, it is possible that the iterative process does not converge or even diverges.
  - Visualizing the Adjoint Solution
    Specific adjoint field functions are available to visualize the adjoint solution.
  - Adjoint Solver Reference
    The adjoint equations are solved with an iterative defect-correction algorithm. For complex problems, there is also the option of adding GMRES and Flexible GMRES stabilization.
  - Adjoint Cost Functions Reference
    An adjoint cost function corresponds to the engineering objective that is examined during the adjoint flow analysis. One example of an engineering objective is to reduce the pressure drop in a piping system. Another example is the reduction of drag force around a car.
  - Mesh Deformation Reference
    You specify the mesh deformation solver properties and define mesh deformation boundary conditions by setting Morpher Specification and Morpher Thin Factor.
  - Adjoint Topology Optimization Model Reference
    The adjoint topology optimization model determines the optimal distribution of material in a specified domain with respect to the optimization objective and constraints, which are defined as adjoint cost functions.
  - Adjoint Field Functions
    The following field functions are made available when computing the adjoint solution and sensitivities.
- Fans and Blowers
  Simcenter STAR-CCM+ provides models for axial and radial fans where classical fan laws apply.
- Virtual Disk Model
  The virtual disk model is based upon the principle of representing propellers, turbines, rotors, fans, and so on, as an actuator disk. The actuator disk treatment is practical when you are concerned about the influence of the rotor/propeller behavior on the flow rather than knowing about the detailed interactions between the flow and the blades of the rotating device.
- Turbulence
  Most fluid flows of engineering interest are characterized by irregularly fluctuating flow quantities.
- Transition
  The term transition refers to the phenomenon of laminar to turbulence transition in boundary layers. A transition model in combination with a turbulence model predicts the onset of transition in a turbulent boundary layer.
- Wall Distance
  Wall distance is a parameter that represents the distance from a cell centroid to the nearest wall face with a non-slip boundary condition. Various physical models require this parameter to account for near-wall effects.
- Radiation
  The Radiation Model is the gateway, or entry point to all of the radiation modeling capabilities of Simcenter STAR-CCM+. This section describes Simcenter STAR-CCM+’s radiation modeling.
- Aeroacoustics
  Aeroacoustics investigates the aerodynamic generation of sound.
- Reacting Flow
  Simcenter STAR-CCM+ provides a selection of models that you can use to simulate a wide range of reacting flow applications.
- Internal Combustion Engines
  In an internal combustion engine (ICE), for example a gasoline engine, the process of combustion takes place in a cylinder (or cylinders) within the engine. The working fluid is a fuel and oxidizer mixture (usually air), which reacts to form combustion products.
- Multiphase Flow
  Multiphase flow is a term which refers to the flow and interaction of several phases within the same system where distinct interfaces exist between the phases. Simcenter STAR-CCM+ considers flow options where phases coexist as: gas bubbles in liquid, liquid droplets in gas, and/or solid particles in gas or liquid, and/or (large scale) free surface flows.
- Dynamic Fluid Body Interaction
  Dynamic Fluid Body Interaction (DFBI) in Simcenter STAR-CCM+ allows you to simulate the motion of a 6-DOF body with the displacement and rotation resulting from the defined mechanical and multiphysics interaction (flow, DEM, solid stress, EMAG).
- Harmonic Balance
  Some unsteady flows have a regularly repeating flow pattern, that is, they are time-periodic. Consider the flow from a fan blade passing across the entrance to a duct. Measurements of the instantaneous flow just within the duct would show a regularly repeating pattern. If the flow disturbances are sufficiently large, and propagate to the end of the duct, measurements of the unsteady flow at any point within the duct show repeating patterns. Such time-periodic patterns can be expressed using Fourier series.
- Solid Stress
  Simcenter STAR-CCM+ allows you to model the response of a solid continuum to applied loads, including mechanical loads and thermal loads that result from changes in the solid temperature.
- Electromagnetism
  Simcenter STAR-CCM+ allows you to model engineering applications involving electromagnetic phenomena. Example applications are electric motors, electric switches, and transformers, which can be modeled based on the classical theory of Electromagnetism.
- Electrochemistry
  Electrochemistry is the study of chemical reactions which occur due to an imposed electrical charge, or a difference in electrical potential at a boundary between a conductor–such as a metal–and an electrolyte. Simcenter STAR-CCM+ provides models that allow you to simulate batteries, corrosion, etching, and other electrochemical reactions.
- Electric Circuits
  Electrical circuits are conducting loops of interconnected electrical components, such as batteries, power sources, resistors, and inductors.
- Plasma
  Plasma is a state of matter similar to a gas that is composed partially or completely of charged particles such as ions and electrons which are not bound to each other.
- Batteries
  You can simulate batteries in Simcenter STAR-CCM+ using battery cells and battery cycling procedures that are defined either directly in Simcenter STAR-CCM+, or in the external software package Simcenter Battery Design Studio.
- Casting
  Casting simulations are performed using transient multiphase simulations using the VOF model with solidification. Conjugate heat transfer is applied between the solidifying melt and the solid mold.
- Region Sources
  This section provides some guidelines on how to use region sources for some common problems.
- Cell Quality Remediation
  The Cell Quality Remediation model helps you get solutions on a poor-quality mesh. This model identifies poor-quality cells, using a set of predefined criteria, such as Skewness Angle exceeding a certain threshold. Once these cells and their neighbors have been marked, the computed gradients in these cells are modified in such a way as to improve the robustness of the solution.
- Guidelines for Applying Simcenter STAR-CCM+
  This part of the documentation provides guidelines on applying Simcenter STAR-CCM+ models to your applications.
- Common Solvers Reference
  In Simcenter STAR-CCM+, solvers compute the solution during the simulation run.

Creating the Adjoint Cost Functions

You define at least one cost function before you start the adjoint analysis. You can also create additional cost functions within the same simulation. Each cost function is solved sequentially in the order they appear under the Adjoint Cost Functions node in the simulation tree.

All cost functions require prior creation of respective reports. These reports define the output quantities associated with the cost functions.

Before you create a cost function:

Create a report that supports adjoint differentiation. For all the available report types, refer to Adjoint Cost Functions Reference. As an example, a force report is created as follows:

To create cost functions:

Right-click the Solvers > Adjoint > Adjoint Cost Functions node and select New.
A Report sub-node is created.

Select the Report node and set Report to the associated report. Only differentiable reports that you have already created appear in the selection list.

Note	Each cost functions is set to Active by default, which means that Simcenter STAR-CCM+ solves for that cost function when you run the adjoint solver. Each active function is solved individually, before proceeding to the next one when one or more stopping criteria are met.