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This paper introduces a predictive control barrier function (PCBF) framework for enforcing state constraints in discrete-time systems with unknown relative degree, which can be caused by input delays or unmodeled input dynamics. Existing…

We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem…

In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…

Control Barrier Functions (CBFs) provide an elegant framework for constraining nonlinear control system dynamics to remain within an invariant subset of a designated safe set. However, identifying a CBF that balances performance-by…

Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…

Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the…

Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…

The traditional finite-difference time-domain (FDTD) method is constrained by the Courant-Friedrich-Levy (CFL) condition and suffers from the notorious staircase error in electromagnetic simulations. This paper proposes a three-dimensional…

We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix…

Computational fluid dynamics (CFD) studies have been increasingly used for blood flow simulations in intracranial aneurysms (ICAs). However, despite the continuous progress of body-fitted CFD solvers, generating a high quality mesh is still…

In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…

Computational Fluid Dynamics (CFD) simulations are often constrained by the memory-bound nature of sparse matrix-vector operations, which eventually limits performance on modern high-performance computing (HPC) systems. This work introduces…

The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the…

Light's spatial degree of freedom is emerging as a potential resource for a myriad of applications, in both classical and quantum domains, including secure communication, sensing and imaging. However, it has been repeatedly shown that a…

We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…

Turbulent flows and fluid-structure interactions (FSI) are ubiquitous in scientific and engineering applications, but their accurate and efficient simulation remains a major challenge due to strong nonlinearities, multiscale interactions,…

We develop a spectral element lattice Boltzmann method (SELBM) with the flux bounce-back (FBB) scheme, to enable accurate simulations of single-phase fluid dynamics in unstructured mesh. We adopt an Eulerian description of the streaming…

There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…

Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation…

Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions…