[CFD Q&A] When simpleFoam Pressure Residual Fails to Converge

I encountered a problem last week that took up quite a bit of time. While running simpleFoam, the pressure residual failed to drop below 1e-3 and, in fact, started to rise. Initially, I thought it might be a mesh issue, but the conclusion turned out to be the relaxation factor.

Problem Situation#

• Software: OpenFOAM v2312
• Geometry: 2D rectangular channel, inlet–outlet boundaries
• Turbulence Model: k-ε (standard)
• Solver: simpleFoam (steady-state)

For the first 20–30 iterations, it seemed to be converging well, but then the pressure residual suddenly began to spike.

Time = 50
 
smoothSolver:  Solving for Ux, Initial residual = 0.0023, Final residual = 1.2e-5, No Iterations 3
smoothSolver:  Solving for Uy, Initial residual = 0.0019, Final residual = 9.8e-6, No Iterations 3
GAMG:  Solving for p, Initial residual = 0.412, Final residual = 0.038, No Iterations 8
time step continuity errors : sum local = 4.2e-5, global = 1.1e-5, cumulative = 3.4e-4
...
Time = 80
 
GAMG:  Solving for p, Initial residual = 0.891, Final residual = 0.21, No Iterations 20

While the velocity was converging smoothly, the pressure remained unstable. This is a typical pattern of pressure-velocity coupling instability.

Root Cause Analysis Process#

Step 1: Check Mesh Quality#

First, I ran checkMesh.

checkMesh -case .

Maximum non-orthogonality was 32 degrees, and max skewness was 0.8 — not bad at all. It didn't seem like a mesh problem.

Step 2: Review Boundary Conditions#

I set the pressure at the inlet to zeroGradient and the outlet to fixedValue 0. These are standard settings, so no issues there.

However, checking the initial p field revealed unusually large values near the inlet. These were remnants from a previous experiment I had conducted using funkySetFields.

Step 3: Check fvSolution#

// fvSolution (original settings)
relaxationFactors
{
    fields
    {
        p               0.7;
    }
    equations
    {
        U               0.9;
        k               0.7;
        epsilon         0.7;
    }
}

U=0.9 is a fairly aggressive value. In SIMPLE, increasing velocity relaxation speeds up convergence, but if the pressure updates cannot keep up, the solution will diverge.

Two causes overlapped:

1. The relaxation factors were excessively high.
2. Incorrect values remained in the initial p field.

Solution#

Lowering Relaxation Factors#

// fvSolution (after modification)
relaxationFactors
{
    fields
    {
        p               0.3;
    }
    equations
    {
        U               0.7;
        k               0.5;
        epsilon         0.5;
    }
}

It is best to start conservatively when running a case for the first time. Once convergence is confirmed, you can gradually increase the values.

Initializing the p Field#

# Cleanly initialize the p file in the 0 directory
cp 0.orig/p 0/p

Alternatively, you can open the 0/p file directly and set it to internalField uniform 0;.

// 0/p
dimensions      [0 2 -2 0 0 0 0];
internalField   uniform 0;
 
boundaryField
{
    inlet
    {
        type            zeroGradient;
    }
    outlet
    {
        type            fixedValue;
        value           uniform 0;
    }
    walls
    {
        type            zeroGradient;
    }
}

Verification#

After the modifications, rerunning the simulation produced the following results:

Time = 50
 
smoothSolver:  Solving for Ux, Initial residual = 0.0018, Final residual = 8.3e-6, No Iterations 3
GAMG:  Solving for p, Initial residual = 0.089, Final residual = 0.0041, No Iterations 5
time step continuity errors : sum local = 2.1e-6, global = 4.3e-7, cumulative = 8.9e-6
 
Time = 200
 
GAMG:  Solving for p, Initial residual = 3.2e-4, Final residual = 1.1e-5, No Iterations 3

By around iteration 200, the pressure residual had stably decreased to the 1e-4 level.

Generalized Lessons#

simpleFoam Convergence Checklist — Use this order to catch most issues:

1. Initial Conditions First: Verify that the p and U fields in the 0/ directory have the intended values. If remnants of previous experiments exist, be sure to initialize them.

2. Conservative Relaxation Factors: Start with defaults like U=0.7, p=0.3. It's safer to confirm convergence before ramping them up. p relaxation especially should be kept low to stabilize the SIMPLE loop.

3. Separate Velocity vs. Pressure Convergence: If U residuals are low but p diverges, it's likely a relaxation issue. If both diverge, check the mesh or boundary conditions first.

4. Monitor GAMG Iterations: If the number of inner iterations required to solve p suddenly increases within the same outer iteration, the convergence direction is likely wrong.

Due to the nature of the pressure correction loop, the SIMPLE algorithm is highly sensitive to relaxation. Always start conservatively — even if it seems slow, ensuring stable convergence before acceleration is ultimately the faster path.

If you are facing similar issues, please share your environment (version, geometry, turbulence model) in the comments. Solutions can vary by case.

Push αp above 0.6 and watch residuals bounce back near iter 30.