Adaptive Upwind Multi-Stencil Scheme for Meshless Flux-Vector-Splitting Methods in Compressible Flow Simulation
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This work presents an adaptive upwind multi-stencil scheme for shock-capturing within meshless flux-vector-splitting (FVS) frameworks for compressible flow simulations. The study aims to improve the robustness and efficiency of meshless upwind discretization while maintaining non-oscillatory shock-capturing. The proposed scheme constructs multiple directional candidate stencils using asymmetric node configurations, enabling mid-point flux approximations to dynamically adapt to discontinuities and complex flow structures. A smoothness-based selection mechanism is introduced to automatically identify the most appropriate stencil, thereby suppressing spurious oscillations while preserving high-order accuracy in smooth regions. The formulation is implemented within a meshless FVS framework using generalized finite difference approximations. Compared with conventional meshless upwind discretization, the present scheme enhances shock resolution capability without introducing complex Riemann solvers, while retaining the intrinsic upwind characteristics of FVS-based methods. Several benchmark problems involving strong discontinuities are investigated to evaluate the performance of the proposed method. Numerical results demonstrate that the adaptive multi-stencil framework achieves high-order accuracy in smooth flow regions and provides non-oscillatory solutions across shocks and contact discontinuities. The proposed scheme offers a promising pathway for developing robust and efficient shock-capturing techniques in meshless computational mechanics.
