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.

Before you begin to compute Adjoint Error Estimates, the solution must have:
  • A converged second-order flow solution
  • Appropriate cost functions
  • A converged second-order Adjoint solution with respect to the desired cost function
The primal solution is computed using a second-order discretization scheme. Using this second-order solution, Simcenter STAR-CCM+ computes the Adjoint Error Estimates as follows:
  1. Recomputes the convective flux of the Navier-Stokes equations by using the MUSCL third-order/CD discretization scheme.
  2. Subtracts the second-order computed cell-residual from the third-order MUSCL cell-residual.

    This difference is a simple estimate of the true numerical error that is present in the second-order solution. The true numerical error of the solution is theoretically calculated by using a higher-order discretization scheme and a fine mesh.

  3. To obtain the Adjoint Error Estimate for each cell, the field of differences in cell-residual from the previous step is multiplied with the Adjoint solution for a given cost function.
Adjoint Error Estimates provide useful information for performing mesh adaption, that is, refinement or coarsening of the mesh. This information is related to a specific cost-function that is associated with that particular error estimate. The estimate can potentially provide an optimally adapted mesh with a minimum cell count and a maximum cost function accuracy.

To compute Adjoint Error Estimates for all defined cost functions:

  1. Right-click the Solvers > Adjoint > Solvers > Adjoint Cost Functions > [cost function] node and select Compute Error Estimates.


    For each defined cost function, an Adjoint Error Estimates > Error Estimate of [cost function] field function becomes available.
    Here, you see a contour plot of the Adjoint Error Estimate of the cost function Force (here defined as force component in the Z direction corresponding to drag). This cost function is applied to the simulation of aerodynamics around a car.

    In locations where the error estimate deviates from zero by a certain threshold, the mesh can be refined to improve the drag.

To analyze the total influence of the discretization error on a cost function:
  1. Create a Sum Report and set Scalar Field Function to Error Estimate of [Cost Function].
    This sum report gives an estimate of the cost function variation as a result of changing the flow convection order of accuracy from second order to MUSCL.