# RISC-Based 10K+ Core Finite Difference Method Accelerator for CFD
## 1 Introduction  
Computational Fluid Dynamics (CFD) plays a pivotal role in modern engineering, particularly in the aerospace industry, where it is widely applied to aerodynamic optimization [1], turbulence modeling [2], and aircraft design [3]. However, driven by complex geometries, transient flow phenomena, and multiphysics coupling, the growing demand for high-fidelity simulations has exposed significant computational bottlenecks [4]. Traditional CPU-based solvers struggle to balance simulation accuracy with practical time constraints, especially when resolving fine-grained spatiotemporal scales or optimizing designs through iterative parametric studies. This limitation stems fundamentally from the mathematical nature of the Navier-Stokes equations (N-S equations), which lack closed-form analytical solutions for virtually all practical flows. Consequently, CFD inherently relies on approximate computational [5] techniques to transform these continuous partial differential equations into discrete algebraic systems solvable by digital computers. The core challenge lies in the inherent computational intensity of this discretization process, where even moderate-sized meshes require trillions of floating-point operations (FLOPS) per timestep [6]. This approximation paradigm--involving spatial discretization (meshing),temporal discretization, iterative solution methods, and often phenomenological turbulence closures--introduces inherent trade-offs between accuracy, computational cost, and physical scope, necessitating advanced hardware to achieve viable high-fidelity solutions. Extensive research has been conducted globally to accelerate CFD simulations. With the integration of thousands of cores on a single chip and superior computational capabilities, graphics processing units (GPUs) have become the predominant architecture in high-performance computing (HPC) [7]. Research scopes have expanded from single-GPU implementations to multi-GPU and cluster-based acceleration [8; 9; 10], encompassing acceleration disparities between explicit and implicit schemes [11; 12], distinctions in structured, unstructured, and hybrid grid characteristics [13], computational impacts of single- versus double-precision arithmetic [14; 15], and the rising prominence of high-order discretization schemes and high-fidelity methodologies [16; 17; 18; 19; 20; 21]. For instance, [PERSON] et al. [22] demonstrated a 9\(\times\) to 16.5\(\times\) speedup over AMD Phenom CPUs by implementing high-order compact finite difference schemes with filtering techniques on Tesla C1060 GPUs for solving compressible Navier-Stokes equations. Similarly, [PERSON] et al. [23] employed second-order MUSCL/NND schemes in Cartesian coordinate systems to accelerate compressible flow solvers, reporting acceleration ratios of 144\(\times\) for NND and 260\(\times\) for MUSCL formats using Tesla P100 GPUs compared to a single E5-2640v4 CPU core. NVIDIA has been a key pioneer in driving and leading the development of general-purpose computing on graphics processing units (GPGPU) technology over the past decade. Numerous numerical methods implemented in CFD solvers have been extensively researched and developed based on NVIDIA's CUDA technology [24; 25; 26; 27]. However, extending existing CFD solvers with CUDA capabilities presents significant challenges. Developers must explicitly define the thread layout (number of blocks, threads per block, etc.) for each kernel function on the GPU, necessitating substantial refactoring of core source code components, which typically demands considerable programming effort. Furthermore, for a production-ready solver, organizations must address both short-term and long-term investment considerations, including costs and returns, alongside platform portability. These factors often deter the adoption of GPU computing for established solution products. As a complementary programming model to CUDA, the OpenACC standard aims to simplify parallel programming for heterogeneous CPU/GPU systems.