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The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
We consider the simulation of isentropic flow in pipelines and pipe networks. Standard operating conditions in pipe networks suggest an emphasis to simulate low Mach and high friction regimes -- however, the system is stiff in these regimes…
Ensemble calculations are essential for systems with uncertain data but require substantial increase in computational resources. This increase severely limits ensemble size. To reach beyond current limits, we present a first-order…
Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…
In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on…
The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
An inverse obstacle problem governed by the Stokes system in the time domain is considered. Two types of extraction formulae about the geometry of an unknown obstacle are given by using the most recent version of the time domain enclosure…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
In this work, we design an entropy stable, finite volume approximation for the ideal magnetohydrodynamics (MHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that…
In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are…
We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…