Finite Difference Implementation of a High-order Space-Time Coupled Compact Gas-Kinetic Scheme

Mathematics > Numerical Analysis [Submitted on 16 Jun 2026] Title:Finite Difference Implementation of a High-order Space-Time Coupled Compact Gas-Kinetic Scheme View PDFAbstract:This study presents a high-order compact finite difference gas-kinetic scheme (FD-CGKS) that introduces a novel spatial discretization strategy for the efficient implementation of space-time coupled high-order schemes on structured grids. A conservative nonlinear compact discretization is achieved by formulating numerical fluxes from physical fluxes at both nodal and interfacial locations. To simplify the multidimensional spatial reconstruction required for the GKS flux evaluation, we propose a dual-grid approach that updates conservative variables on both a primary grid and an identical dual grid, offset by half the mesh spacing. By leveraging the time-accurate interface solutions from the gas-kinetic evolution model, the scheme explicitly updates averaged spatial derivatives between virtual interfaces, naturally enabling compact high-order reconstruction. Furthermore, a nonlinear GENO method is incorporated to capture flow discontinuities with high resolution and robustness, effectively suppressing spurious oscillations. The proposed framework, which also offers new perspectives for designing schemes based on space-time decoupled Riemann solvers, is systematically validated. Comprehensive benchmark computations of inviscid and viscous flows demonstrate the scheme's high accuracy in resolving a wide spectrum of flow features, from smooth multiscale structures to strong shock discontinuities. Current browse context: math.NA References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.