OpenFOAM Tutorial (Chpt 2 — Section 6): fvSchemes + fvSolution Explained | Discretization, Solvers

The full tutorials with supporting Sim files, geometries, documents, and teacher support are placed at Udemy. Please refer there. The courses are really cheap compared to the efforts it took to create them, but if anyone needs to have it free, contact me and I will find a way. StarCCM Courses: https://www.udemy.com/course/star-ccm-expert-applications-vol-1-real-engineering/?referralCode=536C577A98868E316EC9 https://www.udemy.com/course/complete-cfd-simulation-in-starccm-advanced/?referralCode=C05897D188FB69CC8296 https://www.udemy.com/course/star-ccm-for-beginners-from-zero-to-your-first-simulation/?referralCode=EFAD8399E5FE89354471 Other courses we have: https://www.udemy.com/course/openfoam-for-beginners-from-installation-to-real-simulation/?referralCode=C9B5C2ACEDD226EAD49F https://www.udemy.com/course/solidworks-without-the-confusion-a-clear-beginner-course/?referralCode=04CC037F67BFD995F1EA https://www.udemy.com/user/sahar-rouzbahani-2/ ## Title (Chapter 2 — Section 6) **Chapter 2 — Section 6: fvSchemes + fvSolution Explained | Discretization, Solvers, and PISO Settings** ## YouTube Description In this section of **Chapter 2**, we review the two most important numerical setup files in OpenFOAM: ✅ `system/fvSchemes` → how OpenFOAM **discretizes** the governing equations ✅ `system/fvSolution` → how OpenFOAM **solves** the resulting linear systems (matrices) ### 1) fvSchemes — choosing numerical schemes We explain why schemes exist (cell-centered fields need face values, so interpolation is required) and walk through the key dictionaries: * **interpolationSchemes**: how values are interpolated to faces (default: **linear**) * **ddtSchemes**: time discretization (here: **Euler**, first-order) * **gradSchemes**: gradient calculations (e.g., **Gauss linear**) * **divSchemes**: divergence / convection terms (Gauss-based schemes) * **laplacianSchemes**: diffusion term (e.g., **Gauss linear corrected** for non-orthogonality) * **snGradSchemes**: surface-normal gradient schemes (gradients on faces) ### 2) fvSolution — solving the matrices After discretization, OpenFOAM solves large algebraic systems iteratively. We break down: * **pressure solver (p)** settings (e.g., PCG + preconditioner) * **tolerance vs relTol** (absolute vs relative stopping criteria) * **pFinal** with **relTol = 0** to force a properly converged final pressure correction * **velocity solver (U)** settings (e.g., smoothSolver + Gauss–Seidel) * **PISO** coupling controls (here: **nCorrectors = 2**) * **pressure reference**: why **pRefCell** and **pRefValue** are needed (to remove “floating pressure” ambiguity when no fixed-pressure boundary exists) In the next section, we run **icoFoam**, then inspect the time folders and visualize the results. ### Keywords (copy/paste) OpenFOAM fvSchemes, OpenFOAM fvSolution, discretization schemes OpenFOAM, interpolationSchemes linear, ddtSchemes Euler, gradSchemes Gauss linear, divSchemes OpenFOAM, laplacianSchemes Gauss linear corrected, snGradSchemes, icoFoam numerics, PCG solver OpenFOAM, smoothSolver OpenFOAM, tolerance relTol OpenFOAM, pFinal relTol 0, PISO nCorrectors, pRefCell pRefValue, floating pressure OpenFOAM, lid driven cavity icoFoam ### Hashtags #OpenFOAM #CFD #icoFoam #fvSchemes #fvSolution #Numerics #PISO #FluidDynamics #OpenSourceCFD #Engineering #BeginnerCFD