Sunday, June 30, 2024

CFD Simulation Numerics: Relaxation, Residuals, Solvers & Schemes Explained

 I can definitely explain numerics parameters in SimScale, including relaxation type, relaxation factors, residual controls, solvers, and schemes:



Numerics in SimScale

SimScale's numerics settings allow you to control various aspects of how the software solves the complex equations involved in simulations (CFD and Structural Analysis). These settings influence accuracy, convergence, and computational efficiency.

Relaxation

  • Relaxation Type: This determines how much of the difference between the current solution and the solution from the previous iteration is applied during the update process. Options include:

    • False Transient: No relaxation applied (full update).
    • Explicit Relaxation: A factor between 0 and 1 is multiplied by the difference for each variable.
    • Implicit Relaxation: Similar to explicit, but the factor is solver-dependent.
  • Relaxation Factor: This value (between 0 and 1) controls the aggressiveness of the update process in explicit relaxation. A lower value leads to slower but potentially more stable convergence.

Residual Controls

Residuals measure the difference between the current solution and the equations it should satisfy. Smaller residuals indicate a closer solution. You can set absolute tolerances for residuals of different variables:

  • Velocity (U) absolute tolerance: How small the velocity residual needs to be for convergence.
  • Pressure (P) absolute tolerance: Similar to velocity, but for pressure residuals.
  • Turb. kinetic energy (K) absolute tolerance: Tolerance for turbulence kinetic energy residuals (relevant in RANS simulations).
  • Specific dissipation rate (w) absolute tolerance: Tolerance for specific dissipation rate residuals (also relevant in RANS).

Solvers

Solvers are algorithms used to solve the system of equations in your simulation. SimScale offers various options for different variables:

  • Velocity (U) solver: Chooses the algorithm for solving the velocity equation.
  • Pressure (P) solver: Selects the algorithm for solving the pressure equation (often coupled with the velocity solver).
  • Turb. kinetic energy (w) solver: Solver for the turbulent kinetic energy equation (RANS).
  • Specific dissipation rate (w) solver: Solver for the specific dissipation rate equation (RANS).

Schemes

Schemes define how the governing equations are discretized for the solver to handle. Choices include:

  • Convection schemes: For approximating how variables like velocity and turbulence are transported within the flow.
  • Diffusion schemes: Approximate how properties like heat diffuse within the domain.
  • Time integration schemes: For transient simulations, these schemes determine how the solution evolves over time.

Choosing the Right Settings

The optimal settings for these parameters depend on your specific simulation type, mesh quality, and desired accuracy. SimScale provides defaults, but you can adjust them for more advanced simulations. It's recommended to consult SimScale's documentation or seek guidance from their support team for specific recommendations based on your project.

Here are some additional resources that you might find helpful:

  • SimScale Documentation on Numerics: [SimScale CFD Numerics ON simscale.com]
  • SimScale Documentation on Structural Analysis Numerics: [SimScale Structural Analysis Numerics ON simscale.com]

Here's a breakdown of when to use the numerics parameters you mentioned in CFD simulations:

Relaxation

  • Use relaxation:
    • When you encounter convergence issues, especially in the initial stages of the simulation.
    • For highly non-linear problems or problems with large gradients.
  • Start without relaxation:
    • If convergence is smooth, using relaxation might slow down the simulation unnecessarily.
  • Adjust relaxation factor:
    • A lower relaxation factor (closer to 0) helps achieve stability but can be slower.
    • A higher factor (closer to 1) can speed up convergence but might lead to divergence (solution blowing up).

Residual Controls

  • Use absolute tolerances:
    • As a general guideline to monitor convergence. Lower residuals indicate a closer solution to the governing equations.
    • These are not strict stopping criteria, but reaching a certain level of reduction in residuals suggests the solution is approaching convergence.
  • Tighten tolerances gradually:
    • Start with looser tolerances for faster initial convergence.
    • Gradually tighten them as the solution progresses to achieve higher accuracy.

Solvers

  • Choose the solver based on:
    • The specific equations being solved (e.g., pressure-based vs. density-based solvers for incompressible flow).
    • The desired balance between accuracy and computational cost.
    • SimScale often offers different solver options, so consult their documentation for recommendations based on your simulation type.

Schemes

  • Upwind schemes:
    • Generally preferred for problems with convection (transport of a variable) to capture the flow direction.
    • Different upwind schemes offer varying levels of accuracy and computational cost.
  • Central differencing schemes:
    • Can be more accurate for smooth, diffusion-dominated problems but might introduce numerical errors for convective flows.
  • Time integration schemes:
    • Explicit schemes are faster but have a stability limit on the time step size.
    • Implicit schemes are more stable but can be computationally more expensive.
    • The choice depends on the nature of your transient simulation (e.g., highly unsteady vs. slowly evolving).

General Tips

  • Start with SimScale's default settings for a baseline.
  • If you encounter convergence issues, experiment with relaxation first.
  • Adjust residual tolerances and solver/scheme choices only if necessary.
  • Consult SimScale's documentation or support for specific recommendations based on your simulation setup.

Remember, CFD simulations involve a balance between accuracy, convergence, and computational cost. Finding the optimal settings for these numerics parameters is an iterative process and may require some trial and error.

Keywords:

CFD Simulation, Numerics, Relaxation, Relaxation Factor, Residual Controls, Absolute Tolerance, Solvers, Pressure Solver, Velocity Solver, Turbulence Solver, Schemes, Convection Schemes, Diffusion Schemes, Time Integration Schemes, SimScale CFD

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