Related papers: High-Order ADER-DG Hydrodynamics with ExaHyPE: Imp…
We study systems interpolating between the 3D incompressible Euler and electron--MHD equations, given by \begin{equation*} \partial_t B + V \cdot \nabla B = B\cdot \nabla V, \qquad V = -\nabla\times (-\Delta)^{-a} B, \qquad \nabla\cdot B =…
We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive…
The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…
In this paper, we study high-order exponential time differencing Runge-Kutta (ETD-RK) discontinuous Galerkin (DG) methods for nonlinear degenerate parabolic equations. This class of equations exhibits hyperbolic behavior in degenerate…
A simple robust genuinely multidimensional convective pressure split (CPS) , contact preserving, shock stable Riemann solver (GM-K-CUSP-X) for Euler equations of gas dynamics is developed. The convective and pressure components of the Euler…
In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…
We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…
Within OpenFOAM, we develop a pressure-based solver for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations are used to describe…
The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying…
Hyperbolic partial differential equations (PDEs) cover a wide range of interesting phenomena, from human and hearth-sciences up to astrophysics: this unavoidably requires the treatment of many space and time scales in order to describe at…
In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
The versatile Arbitrary-DERivative (ADER) scheme is cast in a multilevel framework (ML-ADER) for fast solution of system of linear hyperbolic partial differential equations. The solution is cycled through spatial operators of varying…
In this paper, we present convergence analysis of high-order finite element based methods, in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts operators. To this end, it is crucial that structure preserving…
To help resolve issues of non-realizability and restriction to homogeneity faced by analytical theories of turbulence, we explore three-dimensional homogeneous shear turbulence of incompressible Newtonian fluids via optimal control and…
In this paper, we construct a new class of blowup solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. In detail, we obtain a class of global rotational exact solutions…
The robust, scalable simulation of flowing electrochemical systems is increasingly important due to the synergy between intermittent renewable energy and electrochemical technologies such as energy storage and chemical manufacturing. The…
Numerical simulations of multidimensional astrophysical fluids present considerable challenges. However, the development of exascale computing has significantly enhanced computational capabilities, motivating the development of new codes…
This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in [14] to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state.…
This work aims at presenting a Discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated…