Hardware-Agnostic Compact Difference Schemes in C++/Kokkos for High-Order CFD

A hardware-agnostic implementation of compact finite difference schemes is presented using the Kokkos programming model, targeting both CPUs (OpenMP) and GPUs (CUDA, HIP) without code duplication. The parallel cyclic reduction (PCR) algorithm achieves significant speedup over the sequential Thomas algorithm on GPUs for large three dimensional grids. For time dependent problems, naive plane by plane execution incurs substantial kernel launch and memory initialization overhead. This is mitigated through a fully batched execution that solves transverse tridiagonal systems simultaneously, yielding up to two orders of magnitude speedup in GPU execution time. The results highlight the necessity of algorithm level redesign when porting legacy Fortran solvers to accelerator architectures. Cross platform numerical solutions agree within machine precision across all CPU and GPU backends, indicating deterministic solver behavior. Comprehensive validation through method of manufactured solutions confirms design order spatial convergence (rates approaching 6.0 for sixth order schemes) and fourth order temporal accuracy with RK4 integration across heat equation, Burgers equation, and isentropic vortex test cases. Long time stability analysis with the isentropic Shu vortex reveals 4th order schemes survive 2 to 5 additional convection periods compared to 6th order schemes before aliasing induced failure. This confirms known filtering requirements for extended simulations. The resulting framework provides verified, performance-portable building blocks for CFD applications requiring high-order accuracy and sustained numerical integrity across evolving compiler and hardware architectures. All development and debugging were performed locally using the OpenMP backend, with total GPU usage limited to fewer than 100 node-hours.