Related papers: Stable higher order finite-difference schemes for …
For computational acoustics, schemes need to have low-dispersion and low-dissipation properties in order to capture the amplitude and phase of the wave correctly. To improve the spectral properties of the scheme, the authors have previously…
We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…
Challenging stellar dynamical problems, such as the study of gravothermal oscillations in star clusters, have in the past initiated the very successful building of GRAPE special purpose computers. It is discussed, that present day tasks…
We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first…
In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…
In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure can not be computed exactly. Instead, we insert a well-chosen state…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds,…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…
The Stokes system with constant viscosity can be cast into different formulations by exploiting the incompressibility constraint. For instance the strain in the weak formulation can be replaced by the gradient to decouple the velocity…
A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled…
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…
The second order weighted and shifted Gr\"{u}nwald difference (WSGD) operators are developed in [Tian et al., arXiv:1201.5949] to solve space fractional partial differential equations. Along this direction, we further design a new family of…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…
This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers…
Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich's…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…