Automated MMS Source Terms — Troubleshooting Guide
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My Mms Source Term simulation is giving me unexpected results — convergence issues, maybe. How do I diagnose this systematically?
Mms Source Term troubleshooting follows patterns once you know what to look for. Most issues fall into three buckets: convergence failures, accuracy problems, and result misinterpretation. Let me give you a systematic diagnostic framework rather than a list of random fixes.
That framing helps. Before we dive in — what's the single most common mistake engineers make with Mms Source Term?
Honestly, it's skipping the sanity checks. Engineers set up a Mms Source Term model, it converges, and they trust the result without verifying it against a hand calculation or a known benchmark. The solver gives you an answer regardless of whether your model is physically correct. Always run a simplified version first.
I lost three days to a failing MMS order test… and the culprit turned out to be a sign error in the source term I derived, not the solver.
Every MMS practitioner walks that road once. MMS audits the solver under the assumption that the source term is correct — so a defect on the source side produces a false conviction. That's why the derivation pipeline needs verification that is independent of the solver. This page organizes the failures at each stage — symbolic derivation, code generation, and injection — by symptom.
Setting: the source \( s = L(u_m) \) is derived symbolically (SymPy or similar) from the manufactured solution \( u_m \) and operator \( L \), emitted as generated code (C/Fortran/UDF), and injected into the solver. Defects anywhere along that chain are our subject; the base procedure is in the consolidated article.
The derived source can be checked numerically, independently of symbolic differentiation. At ~10 random points \( \mathbf{x}_i \) in the domain, compare ① the generated code's \( s(\mathbf{x}_i) \) with ② a high-accuracy finite-difference evaluation of the operator applied to \( u_m \). With central differences at \( h \approx 10^{-5} \), agreement to a relative error around \( 10^{-8} \) is expected — any point worse than that means a derivation or codegen defect. This check takes minutes to write and catches sign errors, coefficient errors, and missing terms almost surely. Make it a mandatory gate before any MMS run.
When the full source disagrees, split the operator and check term by term. For advection-diffusion-reaction:
$$ s = \underbrace{\frac{\partial u_m}{\partial t}}_{s_1} + \underbrace{\mathbf{a}\cdot\nabla u_m}_{s_2} - \underbrace{\nabla\cdot(k\nabla u_m)}_{s_3} + \underbrace{r\,u_m}_{s_4} $$
Checking \( s_1 \)–\( s_4 \) individually pinpoints the bad term. The usual suspects:
| Error class | Typical case | Detection tip |
|---|---|---|
| Sign-convention mismatch | Source on RHS vs. LHS; diffusion-term sign | Rewrite the solver's equation into "source on the right" form before deriving |
| Coefficient definition mismatch | \( \nu \) vs. \( \mu \); divided by \( \rho \) or not; \( \alpha \) vs. \( k \) | Map solver input names/units to your symbol table explicitly |
| Missing terms | Forgotten time derivative (steady derivation, unsteady run); conservative-form remainder \( u\,\nabla\cdot\mathbf{a} \) | Count the terms; decomposition makes a missing term a comparison against zero — instantly visible |
| Coordinate-system mismatch | Cartesian derivation for an axisymmetric solver (missing \( 1/r \) terms) | Write the operator in the solver's coordinates before differentiating |
| Tensor-component mix-ups | Forgotten symmetrization; row/column convention of \( \nabla\mathbf{u} \) | Check per component; write out a small 2-D case fully by eye |
NS-scale equations produce thousands of operations, and code generation grows its own failure modes:
sympy.cse() and emit as chains of intermediatespow(x, 2) to multiplicationsimplify/factor to resolve the cancellation, then re-emitThe injection stage (UDFs, user subroutines) has traps unrelated to derivation:
The strongest diagnostic here is visualizing the spatial error field \( |u_h - u_m| \): derivation errors spread everywhere; injection errors carry structure — bands, zones, boundaries.
So starting with the full equation set is exactly why I couldn't tell what was broken…
Exactly — and veterans build up equation by equation. ① Pure diffusion (Poisson) and confirm the order → ② add advection → ③ add the nonlinear term → ④ add coupling. At every stage you hold the fact "the previous stage passed," so when it breaks, the newest term is the culprit — immediately. Structure the derivation script per term and this build-up doubles as your regression test. Starting cold with full NS is like learning to dive from the ten-meter platform.
Related: automated source-term derivation (consolidated), NS-MMS troubleshooting, convergence-rate troubleshooting.