Strictly causal adaptive Gauss–Hermite velocity resolution with conservative nonnegative remapping

Abstract

We develop a strictly causal adaptive velocity-resolution strategy for a three-dimensional tensor-product Gauss–Hermite discretisation used in a one-dimensional periodic kinetic transport setting. A Q729 main branch and a Q2197 shadow branch are advanced over a short causal horizon, and a low-to-high population defect determines whether the calculation remains on Q729 or is promoted to Q2197. Inter-set transfer is performed by a nonnegative constrained remap that preserves mass, the three momentum components, and total energy. The decision threshold is calibrated once and then frozen. Held-out dense-time, independently varied parameter, and independently prescribed periodic double-interface tests show no underresolved cases at the prescribed population-error tolerance; in the latter benchmark, the frozen gate retained all four moderate cases and promoted all four stress cases without threshold refitting. Higher-order Q3375 and Q4913 comparisons are used to assess macroscopic accuracy, while wall-clock tests quantify both the average speedup and the cases in which shadow overhead removes the benefit. The method is therefore presented as a conservative promotion mechanism with no observed false negatives in the tested datasets, rather than as a universal acceleration guarantee.