Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.34252

A GPU-efficient local ADER finite-difference method for compressible-flow DNS

Hong Zhang·Xian Wang·Xinliang Li·Yibing Chen·Xing Ji
View original source ↗Read source document ↗Export metadata ↓

Abstract

Algorithm design tailored to graphics processing units (GPUs) can substantially improve the efficiency of computational fluid dynamics (CFD) simulations. Efforts to adapt CFD solvers to GPUs often focus on spatial discretization, while time advancement commonly relies on multistage Runge--Kutta (RK) methods. However, these RK methods require repeated residual evaluations and full-domain operations, increasing the cost of compressible-flow direct numerical simulation (DNS). To reduce this overhead, we develop a local arbitrary high-order derivatives (ADER) finite-difference method that couples a compact ten-point quadratic predictor to a conservative central corrector through operator matching. With two quadrature nodes, one Picard correction, and selective dissipation, smooth convective tests recover third-order convergence under fixed-CFL refinement and near-seventh-order spatial behavior when background spatial error dominates. Temporal states remain kernel-local, and halo communication overlaps interior computation. Tests of smooth advection, periodic turbulence, and wall-bounded flows assess accuracy and flow statistics. On a $302^3$-node viscous Taylor--Green benchmark without heat conduction, throughput reaches 230.87 million node updates per second on one V100 GPU in double precision, 1.944 times that of spatially matched three-stage Runge--Kutta integration. Weak-scaling efficiency reaches 99.44\% from 4 to 32 V100 GPUs at 1.812 billion nodes.

Explore related subjects

physics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hong Zhang, Xian Wang, Xinliang Li, Yibing Chen, Xing Ji. 2026-10-25. A GPU-efficient local ADER finite-difference method for compressible-flow DNS. https://arxiv.org/abs/2610.34252

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

sft-wick: A formalism and package for Feynman-diagram expansion and evaluation in stochastic field theories

When stochastic field dynamics are cast into a path-integral formulation, perturbation theory becomes systematic but the resulting expansion quickly grows combinatorially large. The setting targeted here includes fields with several components and several dimensions, matrix propagators, tensor-valued couplings, and non-Gaussian driving noise specified by arbitrary n-point cumulants. Wick pairings grow factorially, and component indices must be routed through the tensor-valued vertices. The useful output is not a raw contraction list, but a diagram table: one entry per topology, with multiplicities, coupling sums, signs, and causal constraints resolved. We present sft-wick, an open-source Python package that constructs these diagram tables and computes their integrals numerically. Given an action and an observable, it enumerates topologically distinct Feynman diagrams, derives their algebraic coefficients, and evaluates the resulting diagram integrals from user-supplied response and cumulant functions. The core algorithm enumerates spatial topologies before routing component indices, avoiding contraction-by-contraction Wick expansion. Response-field constraints, including vanishing response-response contractions, the Ito prescription, and the absence of causal response loops, are enforced during enumeration. Predictions are validated against direct Langevin simulations in two worked examples, with Gaussian and with non-Gaussian driving noise, and agree with the simulations within stated error budgets.

physics.comp-ph↗
arXiv2026

A neural accelerated roughness-resolved Discrete Element Method (Rough-DEM) for modeling granular systems

The Discrete Element Method (DEM) is an indispensable tool for modeling and understanding the basic mechanical behaviors of (dry) granular media, a class of disordered material systems of significant interest to multiple scientific domains from (geo-)physics to (chemical) engineering. At the core of all present DEM frameworks is a phenomenological friction law--commonly chosen to be of the Amontons-Coulomb type--that models the frictional interaction among constituent grains. Here, inspired by research in the tribology community, we present an alternative, fundamentally different framework, termed roughness-resolved DEM (Rough-DEM), in which contact friction is handled in a more physics-based manner. In this framework, instead of using a friction law, we explicitly resolve the surface topography of each grain and let friction emerge from collective frictionless interactions of surface asperities. In essence, we trade phenomenology for physics at the cost of an increased computational demand. To mitigate the cost, we introduce an FE$^2$-like algorithm and a feature-wise linear modulation (FiLM)-based neural network surrogate, both of which are parallelized on GPU to accelerate contact computation. Crucially, using this framework in 2D, we (1) demonstrate the possibility of recovering a two-body-based Amontons-Coulomb-type friction behavior using a \textit{simple} representation of surface topography, and (2) identify many-body-based frictional behaviors--more specifically, the angle of repose values--that \textit{cannot always} be captured by current DEM frameworks under the same level of model complexity. We conclude by discussing future directions for Rough-DEM, as well as exciting new opportunities it could unlock for a wide range of emerging applications, including (designing) suspension rheology and metamaterial mechanics.

physics.comp-ph↗
arXiv2026

Fast diagonalization for matrix-free inversion of the nodal even-parity operator in hybrid finite element SPN transport

The hybrid finite element method stores a dense inverse of the nodal even-parity operator for every node and energy group, and that storage limits the spatial and angular expansion orders, more tightly still on a GPU, whose memory is smaller than that of a host. This work introduces fast diagonalization for the nodal even-parity operator of the hybrid finite element SPN method: the stored dense inverse is replaced by the eigendecompositions of a planar, an axial and an angular factor, and the inverse is applied without being formed explicitly. Every even-parity moment of the SPN equations obeys an equation of the same diffusion form, with no mixed derivatives, so the angular coupling is the same in every spatial direction. On a node extruded along the axis, the operator is then an exact Kronecker sum of the three factors. The factorization merely recasts the computation, so the discretization and the solution are unchanged, and the nodes are not required to be identical to one another. The method is implemented for CPU and GPU hardware and compared with the dense inverse within one solver. On a pressurized water reactor core in SP3, the two paths agree to within round-off error, the storage falls from 3.76 GB to 821 kB, and the calculation is 4.15 times faster. On a 33-group fast reactor core, the dense inverse would occupy 24.9 GB and the dense path would need more memory than both the device and the host provide, whereas the factors occupy only 1.26 MB, so the solution can be obtained. The factorization thus reduces the storage of the nodal inverse by more than three orders of magnitude and brings multigroup core calculations at their required spatial expansion orders within the memory of a single GPU.

physics.comp-ph↗