arXiv subjects

Bjørn Wu

Publications and source records attributed to Bjørn Wu.

3 recordsLinked to original sources

arXiv2026

A Log-Gaussian Scale-Space Limiter for Hybrid Continuum--Ballistic Gas Dynamics

We propose a log-Gaussian scale-space limiter for hybrid continuum--ballistic gas dynamics. The method defines complementary continuum and ballistic weights as Gaussian cumulative probabilities in logarithmic Knudsen-number space and blends Navier--Stokes--Fourier and half-range Maxwellian kinetic fluxes. The method is formulated as a lightweight hybrid closure intended for future implementation in finite-volume, discrete Boltzmann, or gas-kinetic solvers. Reduced one-dimensional closure/profile comparisons against DVM/BGK Fourier and Couette data show that log-Gaussian weighting of NSF and jump/slip-corrected branches improves the tested macroscopic profiles relative to NSF. The same six DVM/BGK profiles are used both as reference profiles and to calibrate K0 and sigma; therefore, the approximately 40 percent reduction in combined mean profile error is an in-sample calibration result for the reduced profile model rather than independent validation or numerical validation of the proposed finite-volume face flux. Additional diagnostics assess non-equilibrium moments, internal parameter robustness, and shock-layer activation.

math.NA↗

arXiv2026

Central-Hermite Sensing and Collision for Frame-Robust Order-Resolved Relaxation on D3Q125

Raw-Hermite sensing and collision on a fixed discrete-velocity set can convert a uniform translation into artificial coupling between nominally distinct nonequilibrium orders. We develop a central-Hermite formulation for a D3Q125 kinetic model with order-resolved log-Gaussian relaxation and compare three variants: raw sensing/raw collision (A), central sensing/raw collision (B), and central sensing/central collision (C). In homogeneous translated second-order perturbations, model C preserves third- and fourth-order modal purity to machine precision, whereas A and B develop boost-dependent cross-order content. Across a grid-CFL-boost matrix, model C reduces the post-transport collision frame discrepancy relative to A by 65.342-98.102% (median 81.131%) in the total relative L-infinity measure. Long-time calculations remain positive and conservative to numerical precision, although the accumulated benefit is configuration dependent because transport continually re-injects frame error. A transport study further reveals a clear trade-off: central-Hermite interface reconstruction strongly suppresses the third-order discrepancy but amplifies the fourth-order discrepancy. The fully central-Hermite collision therefore substantially reduces collision-induced cross-order frame discrepancy, while residual dependence remains due to discrete transport and finite velocity-space representation. This moment-space improvement does not by itself establish a comparable reduction in macroscopic Galilean transport error.

math.NA↗

arXiv2026

Hierarchical Log-Gaussian Relaxation on a Fixed D3Q125 Velocity Set

We develop a hierarchical order-resolved relaxation model for a fixed D3Q125 discrete-velocity kinetic formulation. Conventional adaptive collision models often use one scalar rarefaction or nonequilibrium indicator for all retained moment orders, thereby coupling distinct kinetic sectors. Here, a shared macroscopic-gradient background is combined separately with second-, third-, and fourth-order thermodynamic nonequilibrium indicators to define effective measures K2, K3, and K4, each driving its own log-Gaussian relaxation spectrum. Pure-order perturbation tests verify selective activation, with nonmatching sectors remaining at roundoff level. Homogeneous mixed-order, amplitude, and composition tests show lower residual nonequilibrium than a common-sensor model while preserving positive populations. In a smooth periodic compression wave at the stated reference discretization and in the TNE-only sensor limit, the peak total nonequilibrium intensity is reduced by 6.565%, with reductions throughout the domain and in all retained moment sectors. Additional timestep, transport-discretization, relaxation-spectrum, uniform-boost, long-time, and shear-wave studies show that the sign of the hierarchical correction is robust over the tested configurations, while its magnitude depends on timestep, transport scheme, sensor frame, and relaxation spectrum. Quantitative boost checks identify the laboratory-frame raw-Hermite origin of the frame sensitivity without detecting an evident collision-path inconsistency over the tested range. The periodic benchmarks preserve the principal global invariants to floating-point accuracy and remain positive. These results establish the mechanism, selectivity, and numerical behavior of order-resolved activation on a fixed velocity set; independent kinetic-reference validation is still required before claiming universal accuracy improvement.

math.NA↗