Related papers: Split-explicit external mode solver in finite volu…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
In this work, we study long-time numerical integration of Hamiltonian systems subject to linear perturbations. By introducing an energy-induced metric, we establish a straightforward, coordinate-free criterion for dissipativity that ensures…
We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier-Stokes equations,…
We present the One-orbital Ensemble Self-Consistent Field (OE-SCF) method, an {alternative} orbital-free DFT solver that extends the applicability of DFT to system sizes beyond the nanoscale while retaining the accuracy required to be…
Empirical observations show that turbulence exhibits a broad range of scaling exponents, characterizing how the velocity gradients diverge in the inviscid limit. These exponents are thought to be linked to singular solutions of the Euler…
In this article we design a finite volume semi-implicit IMEX scheme for the incompressible Navier-Stokes equations on evolving Chimera meshes. We employ a time discretization technique that separates explicit and implicit terms which…
A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first order hyperbolic formulation of continuum fluid and solid mechanics. The scheme provably respects the stiff…
The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled…
High Peclet number, turbulent convection is a classic system with a large timescale separation between flow speeds and the thermal relaxation time. In this paper, we present a method of fast-forwarding through the long thermal relaxation of…
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…
We evaluate the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations. The methods are based on affine combinations of time-splitting integrators and…
We present a new parallel spectral element solver, FNPF-SEM, for simulating linear and fully nonlinear potential flow-based water waves and their interaction with offshore structures. The tool is designed as a general-purpose wave model for…
We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…
We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…
The split-operator pseudo-spectral method based on the fast Fourier transform (SO-FFT) is a fast and accurate method for the numerical solution of the time-dependent Schr\"odinger-like equations (TDSE). As well as other grid-based…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces…
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…
A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The model is a solution of the full three-dimensional equations…
The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In particular, the divergence-free condition and boundary…