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Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…
Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a…
All major weather and climate applications are currently developed using languages such as Fortran or C++. This is typical in the domain of high performance computing (HPC), where efficient execution is an important concern. Unfortunately,…
High-level programming languages such as Python are increasingly used to provide intuitive interfaces to libraries written in lower-level languages and for assembling applications from various components. This migration towards…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
Hybrid Reynolds-averaged Navier Stokes large eddy simulation (RANS LES) methods have become popular for simulation of massively separated flows at high Reynolds numbers due to their reduced computational cost and good accuracy. The current…
Efficiently solving large-scale linear systems is a critical challenge in electromagnetic simulations, particularly when using the Crank-Nicolson Finite-Difference Time-Domain (CN-FDTD) method. Existing iterative solvers are commonly…
The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have…
While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier--Stokes closure operators using forced direct numerical simulations, MFM can also be…
This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…
Simulating turbulence is critical for many societally important applications in aerospace engineering, environmental science, the energy industry, and biomedicine. Large eddy simulation (LES) has been widely used as an alternative to direct…
Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through…
We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…
Numerical simulations can help solve complex problems. Most of these algorithms are massively parallel and thus good candidates for FPGA acceleration thanks to spatial parallelism. Modern FPGA devices can leverage high-bandwidth memory…
This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on…
We seek possible statistical consequences of the way a forcing term is added to the Navier--Stokes equations in the Direct Numerical Simulation (DNS) of incompressible channel flow. Simulations driven by constant flow rate, constant…
We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the…
MPI's derived datatypes (DDTs) promise easier, copy-free communication of non-contiguous data, yet their practical performance remains debated and is often reported only for a single MPI stack. We present a cross-implementation assessment…
We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned…
We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…