Related papers: THC: a new high-order finite-difference high-resol…
Modeling fluid turbulence using a 'skeleton' of coherent structures has traditionally progressed by focusing on a few canonical experiments, such as pipe flow and Taylor-Couette flow. We here consider an alternative canonical experiment,…
In this paper a new semi-implicit relaxation scheme for the simulation of multi-scale hyperbolic conservation laws based on a Jin-Xin relaxation approach is presented. It is based on the splitting of the flux function into two or more…
Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first…
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control.…
The long term magnetohydrodynamic stability of magnetized transonic/supersonic jets is numerically investigated using a spatial approach. We focus on two-dimensional linearly-unstable slab configurations where the jet is embedded in a…
We have studied forced turbulence of compressible magnetohydrodynamic (MHD) flows through two-dimensional simulations with different numerical resolutions. First, hydrodynamic turbulence with Mach number $<M_s >_{\rm init} \equiv < v >_{\rm…
Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and…
This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…
In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristic-wise approach, the scheme switches the numerical flux of each characteristic…
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…
The accurate numerical simulation of high Reynolds number incompressible flows is a challenging topic in computational fluid dynamics. Classical inf-sup stable methods like the Taylor-Hood element or only $L^2$-conforming discontinuous…
We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
This paper aims at developing exactly energy-conservative and structure-preserving finite volume schemes for the discretisation of first-order symmetric-hyperbolic and thermodynamically compatible (SHTC) systems of partial differential…
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…
High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…
We present nsCouette, a highly scalable software tool to solve the Navier-Stokes equations for incompressible fluid flow between differentially heated and independently rotating, concentric cylinders. It is based on a pseudospectral spatial…
We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\sc S. Chu, A. Kurganov, and I. Menshov}, Appl. Numer. Math.,…
Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep…
Discontinuous Galerkin (DG) methods coupled to WENO algorithms allow high order convergence for smooth problems and for the simulation of discontinuities and shocks. In this work, we investigate WENO-DG algorithms in the context of…