Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
Efficient Implementation of Essentially Non-oscillatory Shock-Capturing Schemes
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Two modifications to the diffuse-interface method for insoluble surfactant modeling avoid sharp-gradient derivatives and decouple delta-function width from interface width, improving accuracy and conserving mass in two-phase flow simulations.
Adaptive high-order and low-order dissipative fluxes augment central-difference schemes to enforce scalar boundedness in multi-component turbulent flows with minimal added dissipation.
An adaptive reconstruction method combines a contact discontinuity detector with THINC for phasic densities and central schemes for tangential velocities to capture material interfaces more sharply in viscous compressible multicomponent flow simulations.
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.
Implements advanced GRMHD numerical techniques in Athena++ and demonstrates them via simulations of magnetically arrested disks around black holes.
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Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods
Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.