💥💥💥 How to fix "overflow" error in Ansys CFD?

 The error “overflow” in Ansys CFD means that a number is being generated that is too large to store. It could be related to dividing a number by a very small number. Some possible ways to fix this error are¹:

• Review the boundary conditions to make sure they are reasonable and consistent with the physical problem.
• Run the simulation in double precision mode, which can handle larger numbers and improve the accuracy of the solution.
• Try using a smaller time step or a different time scale factor, which can help avoid numerical instability and convergence issues.
• Try using a different turbulence model, such as SST, which can better capture the flow physics and reduce numerical errors.
• Try using a different advection scheme, such as High Resolution or Upwind, which can reduce numerical diffusion and oscillations.

What is numerical instability?

Numerical instability is a concept that refers to the tendency of some numerical algorithms or procedures to produce inaccurate or unreliable results due to errors in the computation. These errors may be caused by factors such as round-off errors, truncation errors, or ill-conditioning of the problem. Numerical instability can lead to large deviations from the expected or exact solution, and sometimes even to divergence or failure of the algorithm. Numerical stability is a desirable property of numerical algorithms, which means that the errors do not significantly affect the final result. Numerical stability depends on both the algorithm and the problem being solved. Some algorithms are more robust than others, and some problems are more sensitive than others. Numerical stability can be assessed by various criteria, such as forward error, backward error, condition number, or error propagation. For more information and examples of numerical instability and stability, you can refer to the web search results¹²³. 

How can I improve numerical stability in my simulation?

There are several ways to improve numerical stability in your simulation, depending on the cause and nature of the instability. Some general tips are:

• Review your mesh quality and resolution, and make sure they are adequate for capturing the flow features and gradients. A poor mesh can introduce numerical errors and instability. You can use mesh adaptation techniques to refine the mesh in regions of interest¹.
• Choose appropriate boundary conditions and initial conditions that are consistent with the physical problem and the expected solution. Inappropriate or unrealistic boundary conditions can cause spurious oscillations or divergence in the solution¹.
• Use relaxation factors to control the rate of change of the solution variables during the iteration process. Relaxation factors are coefficients that dampen the effect of the new computed values on the old values. A smaller relaxation factor can improve stability, but it can also slow down convergence. A larger relaxation factor can speed up convergence, but it can also cause instability. The optimal relaxation factor depends on the problem and the solver, but a typical range is between 0.15 and 0.7².
• Use a suitable time step size and time integration scheme for transient simulations. A too large time step size can cause numerical instability and loss of accuracy. A too small time step size can increase the computational cost and time. A good practice is to use a time step size that satisfies the Courant-Friedrichs-Lewy (CFL) condition, which relates the time step size to the spatial discretization and the flow velocity. The CFL number is defined as CFL = uδt/δx, where u is the flow velocity, δt is the time step size, and δx is the spatial discretization. A CFL number less than 1 is usually recommended for stability³. The time integration scheme can also affect stability and accuracy. For example, an explicit scheme can be more unstable than an implicit scheme, but it can also be more accurate for some problems³.
• Use a suitable spatial discretization and advection scheme for convective terms. The spatial discretization determines how the solution variables are interpolated or extrapolated at the cell faces from the cell centers. The advection scheme determines how the convective fluxes are calculated at the cell faces from the solution variables. Different schemes have different levels of accuracy, stability, and computational cost. For example, a first-order upwind scheme can be more stable than a second-order central difference scheme, but it can also introduce more numerical diffusion and smearing of sharp gradients³.

These are some of the common ways to improve numerical stability in your simulation. 

Can you explain more about relaxation factors?

Sure, I can explain more about relaxation factors. Relaxation factors are coefficients that control the amount of change in the solution variables during the iterative process of solving a system of equations. They are used to improve the stability and convergence of the solution, especially for nonlinear and complex problems. Relaxation factors can be either under-relaxation or over-relaxation, depending on whether they are less than or greater than one. Under-relaxation means that only a fraction of the predicted change in the solution variable is applied, which can slow down the convergence but increase the stability. Over-relaxation means that more than the predicted change in the solution variable is applied, which can speed up the convergence but decrease the stability. The optimal value of the relaxation factor depends on the problem and the algorithm, and it is usually determined by trial and error. Some common ranges of relaxation factors are between 0.15 and 0.7 for flow variables, and between 0.5 and 1 for turbulence variables¹. Relaxation factors are often used in CFD simulations, where they can affect the accuracy and efficiency of the solution. For example, relaxation factors can help avoid numerical instability and divergence in steady-state simulations, or reduce numerical diffusion and oscillations in transient simulations². Relaxation factors are also related to the time step size and the spatial discretization schemes, which can also influence the stability and accuracy of the solution³. 

How do I choose the optimal relaxation factor?

Choosing the optimal relaxation factor in Ansys CFD depends on the problem and the algorithm you are using, and it is usually determined by trial and error. There is no universal rule for selecting the best value, but some general guidelines are¹²³:

• A relaxation factor that is too small (< 0.15) can slow down the convergence rate and increase the computational cost.
• A relaxation factor that is too large (> 0.7) can cause numerical instability and divergence of the solution.
• A relaxation factor that is close to 1 (no relaxation) can sometimes improve the accuracy of the solution, but it can also introduce numerical errors and oscillations.
• A relaxation factor that is close to 0 (full relaxation) can sometimes improve the stability of the solution, but it can also introduce numerical diffusion and smearing of sharp gradients.

Therefore, a good practice is to start with a moderate value of the relaxation factor (between 0.3 and 0.7) and then adjust it according to the behavior of the solution. You can monitor the residuals, the convergence history, and the physical quantities of interest to see if the solution is stable, accurate, and realistic. You can also use the auto-relaxation feature in Ansys CFD, which can dynamically change the relaxation factor for the flow variables to speed up convergence while trying to keep the solution stable². However, this feature may not work for all problems, and you may need to try different values manually to find the optimal one.

Can you explain more about auto-relaxation feature?

Sure, I can explain more about the auto-relaxation feature in Ansys CFD. Auto-relaxation is a technique that automatically adjusts the relaxation factors for the flow variables during the iterative process of solving the system of equations. Relaxation factors are coefficients that control the rate of change of the solution variables from one iteration to the next. They are used to improve the stability and convergence of the solution, especially for nonlinear and complex problems. A smaller relaxation factor can increase stability, but it can also slow down convergence. A larger relaxation factor can speed up convergence, but it can also cause instability. The optimal relaxation factor depends on the problem and the algorithm, and it is usually determined by trial and error.

The auto-relaxation feature is designed to dynamically change the relaxation factor for each flow variable based on its residual behavior. The residual is a measure of how well the solution satisfies the equation for each variable. A lower residual means a more accurate solution. The auto-relaxation feature tries to find the optimal balance between stability and convergence by increasing or decreasing the relaxation factor according to the residual trend. For example, if the residual is decreasing steadily, the auto-relaxation feature will increase the relaxation factor to speed up convergence. If the residual is oscillating or increasing, the auto-relaxation feature will decrease the relaxation factor to improve stability.

The auto-relaxation feature can be enabled or disabled in Ansys CFD by selecting or deselecting the Auto Relaxation option in the Numerics panel¹. The auto-relaxation feature can sometimes improve the convergence rate and efficiency of the solution, but it may not work for all problems. In some cases, if the auto-relaxation feature causes divergence or instability, it is recommended to try with manual relaxation factors that are fixed over the iterations². You can also monitor and adjust the relaxation factors manually by using the Relaxation Factors option in the Numerics panel¹.