Abstract:Conservation laws are conventionally discretized through floating-point flux evaluation, with invariants obtained by cancellation of approximate interface contributions and admissible weak solutions selected by reconstruction and Riemann solvers. Here we introduce an operator-level formulation in which conservative dynamics is realized as an exact discrete interaction rule on a quantized state space. The update is defined by an antisymmetric integer-transfer operator, which enforces conservation exactly at the arithmetic level and eliminates round-off drift from the primitive evolution. For scalar laws, monotone order-preserving transfers select admissible shock structures within the primitive update, rather than through flux reconstruction. Numerical experiments show that the interaction rule preserves high-frequency transport near the Nyquist limit and maintains sharply localized discontinuities in Burgers dynamics. The same construction extends to multidimensional problems and systems of conservation laws through oriented, vector-valued integer transfers. The results show that exact integer-transfer dynamics can suppress cumulative transport drift while preserving entropy-shock localization in nonlinear conservative evolution.
From: Park Junhu [view email]
[v1]
Wed, 29 Apr 2026 07:50:08 UTC (106 KB)
[v2]
Sun, 10 May 2026 06:41:25 UTC (35 KB)
[v3]
Thu, 28 May 2026 01:32:28 UTC (24 KB)
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