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The paper presents novel results, obtained on the basis of the modified theory of hydraulic fractures (HF). The theory underlines significance of the speed equation. When applied to numerical simulation of HF, the theory reveals three…
The design of microfluidic devices is a cumbersome and tedious process that can be significantly improved by simulation. Methods based on Computational Fluid Dynamics (CFD) are considered state-of-the-art, but require extensive compute time…
Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the…
In this paper, we define and analyze a subclass of (time-invariant) Control Barrier Functions (CBF) that have favorable properties for the construction of uniformly timevarying CBFs and thereby for the satisfaction of uniformly time-varying…
For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to…
In order to enable simulations of developing wind turbine array boundary layers with highly realistic inflow conditions a concurrent precursor method for Large Eddy Simulations is proposed. In this method we consider two domains…
This work develops a robust adaptive control strategy for discrete-time systems using Control Barrier Functions (CBFs) to ensure safety under parametric model uncertainty and disturbances. A key contribution of this work is establishing a…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
A numerical method for the direct numerical simulation of incompressible wall turbulence in rectangular and cylindrical geometries is presented. The distinctive feature resides in its design being targeted towards an efficient…
We propose a new computational framework that combines the recently developed time-parallel (TP) and the compound wavelet matrix (CWM) methods. The framework, termed tpCWM, offers significant computational acceleration by making…
White paper: The aim of this work is to apply and analyze machine learning methods for uncertainty quantification of turbulence models. In this work we investigate the classical and data-driven variants of the eigenspace perturbation…
We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain,…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin (DG) solution of hyperbolic conservation laws on adaptive moving meshes that typically employs explicit stepping. A commonly…
This text presents one of the first successful applications of a rare events method for the study of multistability in a turbulent flow without stochastic energy injection. The trajectories of collapse of turbulence in plane Couette flow,…
A new computational methodology, termed "PeleLM-FDF" is developed and utilized for high fidelity large eddy simulation (LES) of complex turbulent combustion systems. This methodology is constructed via a hybrid scheme combining the Eulerian…
Many natural and industrial turbulent flows are subjected to time-dependent boundary conditions. Despite being ubiquitous, the influence of temporal modulations (with frequency $f$) on global transport properties has hardly been studied.…
Accurate and efficient prediction of extreme ship responses continues to be a challenging problem in ship hydrodynamics. Probabilistic frameworks in conjunction with computationally efficient numerical hydrodynamic tools have been developed…
The two-step backward differential formula (BDF2) with unequal time-steps is applied to construct an energy stable convex-splitting scheme for the Cahn-Hilliard model. We focus on the numerical influences of time-step variations by using…
We employ the principle of minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first…