ARCTIC SYSTEMSHEAT TRANSFER · METHODS & VERIFICATIONTECHNICAL DOCUMENTATION / REFERENCES
The physical laws and numerical ideas are established. Our contribution is their implementation, testing and application within the stated scope.
S. V. Patankar (1980). Numerical Heat Transfer and Fluid Flow.
Foundational numerical treatment of transport and control-volume balances. A background reference, not a claim that every algorithm in the book is implemented here.
Publisher record ↗C. R. Swaminathan & V. R. Voller (1993). On the enthalpy method. International Journal of Numerical Methods for Heat & Fluid Flow, 3(3), 233–244.
Background on enthalpy formulations and their relation to apparent heat capacity and source-based approaches. We do not claim to reproduce the paper's optimal scheme.
DOI ↗ · Author institution record ↗A. N. Tikhonov & A. A. Samarskii (1958). On homogeneous difference schemes. Doklady Akademii Nauk SSSR, 122(4), 562–565.
Historical mathematical context. This citation does not identify our FVM implementation as a particular Tikhonov–Samarskii scheme or transfer a convergence theorem to our code.
Mathematical Institute record ↗F. Moukalled, L. Mangani & M. Darwish (2016). The Finite Volume Method in Computational Fluid Dynamics. Springer.
Reference for control-volume discretization, diffusion, boundary treatment and algebraic systems. Its wider CFD capabilities are not features of this thermal solver.
Book and chapter contents ↗K. Salari & P. Knupp (2000). Code Verification by the Method of Manufactured Solutions. SAND2000-1444.
Methodological reference. Our selected multidimensional fields and source terms are our test constructions, not a standardized international benchmark dataset.
Sandia record ↗The Neumann solution of the two-phase Stefan problem provides the analytical reference. A publicly accessible formulation appears in N. Tubini, S. Gruber & R. Rigon (2021), The Cryosphere, 15, 2541–2568, §4.1, equations 27–29.
This is a modern presentation of a classical solution. The authors' nonlinear algorithm is not the one implemented here; this citation is not a comparison with their software.
Reference equations ↗V. R. Voller & C. R. Swaminathan (1993). Treatment of discontinuous thermal conductivity in control-volume solutions of phase-change problems. Numerical Heat Transfer, Part B, 24(2), 161–180.
Related literature on the Kirchhoff transformation and intercell conductivity. The author record and abstract were checked; equivalence of our implementation to the paper’s full algorithm has not been established.
DOI ↗These references identify methodological foundations and benchmark formulations. They do not constitute third-party endorsement, peer review of this solver or proof of accuracy outside the documented tests.