Darrieus–Landau instability is an essential driving mechanism behind flame acceleration, especially in the absence of turbulence. Effectively quiescent initial conditions are particularly relevant for explosion safety in various process facilities or parts of nuclear power plants. Large-scale industrial facilities pose a considerable challenge for numerical modeling through CFD since applying methods that rely on resolving the internal flame structure to predict the flame dynamics is well outside the limits of today’s computational resources. Therefore, in present work, a new scale-adaptive URANS (Unsteady Reynolds-Averaged Navier–Stokes) model for sub-grid closure is introduced. It is aimed at modeling the effects of the Darrieus–Landau instability at a significantly reduced computational cost. Model validation was performed using lean and stoichiometric hydrogen deflagration experiments at medium ( $\sim 1m$) and large ( $\sim 10m$) geometric scales.

The QR factorisation is a cornerstone of numerical linear algebra, essential for solving overdetermined linear systems, eigenvalue problems, and various scientific computing tasks. However, computing it for ill-conditioned tall-and-skinny (TS) matrices on large-scale distributed-memory systems, particularly those with multiple GPUs, presents significant challenges in balancing numerical stability, high performance, and efficient communication. Traditional Householder-based QR methods provide numerical stability but perform poorly on TS matrices due to their reliance on memory-bound kernels. This paper introduces a novel algorithm for computing the QR factorisation of ill-conditioned TS matrices based on CholeskyQR methods. Although CholeskyQR is fast, it typically fails due to severe loss of orthogonality for ill-conditioned inputs. To solve this, our new algorithm, mCQRGSI+, combines the speed of CholeskyQR with stabilising techniques from the Gram–Schmidt process. It is specifically optimised for distributed multi-GPU systems, using adaptive strategies to balance computation and communication. Our analysis shows the method achieves accuracy comparable to Householder QR, even for extremely ill-conditioned matrices (condition numbers up to ${10}^{16}$). Scaling experiments demonstrate speedups of up to $12\times$ over ScaLAPACK and $16\times$ over SLATE’s CholeskyQR2. This work delivers a method that is both robust and highly parallel, advancing the state-of-the-art for this challenging class of problems.