Enforcing the Courant-Friedrichs-Lewy condition in explicitly conservative local time stepping schemes

  title={Enforcing the Courant-Friedrichs-Lewy condition in explicitly conservative local time stepping schemes},
  author={Nickolay Y. Gnedin and Vadim A. Semenov and Andrey V. Kravtsov},
  journal={J. Comput. Phys.},

A High-Order, Conservative Integrator with Local Time-Stepping

A family of multistep integrators based on the Adams-Bashforth methods, intended for use in solving conservative PDEs in discontinuous Galerkin formulations, but are applicable to any system of ODEs.

On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations

In this study, standard and non-standard finite-difference methods are proposed for numerical solutions of the time-spatial fractional generalized Newell-Whitehead-Segel equations describing the

Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid

In this paper, a first-order projection method is used to solve the Navier–Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity.

The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers

A new framework for adaptive mesh refinement calculations that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation is described.

The AREPO Public Code Release

This version contains a finite-volume magnetohydrodynamics algorithm on an unstructured, dynamic Voronoi tessellation coupled to a tree-particle-mesh algorithm for the Poisson equation either on a Newtonian or cosmologically expanding spacetime.

Stability analysis of discrete population balance model for bubble growth and shrinkage

The stability condition for solving the population balance equation (PBE) involving bubble growth and shrinkage within the Eulerian framework is proposed. The particle flux weighted average Courant

Appraising scattering theories for polycrystals of any symmetry using finite elements

This paper uses three-dimensional grain-scale finite-element (FE) simulations to appraise the classical scattering theory of plane longitudinal wave propagation in untextured polycrystals with

An Optimized Control Approach for HIFU Tissue Ablation Using PDE Constrained Optimization Method

  • Xilun LiuM. Almekkawy
  • Engineering
    IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
  • 2021
The simulation results for all cases indicate the robustness and the computational efficiency of the proposed method compared to the steepest gradient descent method with the closed-form solution.



A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi Dimensions

In numerical simulations for the two-dimensional compressible Navier-Stokes equations, the efficiency and the optimal order of convergence being p+1, when a polynomial approximation of degree p is used.

Multirate Explicit Adams Methods for Time Integration of Conservation Laws

This paper constructs multirate linear multistep time discretizations based on Adams-Bashforth methods that is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - V. Local time stepping and p-adaptivity

The proposed LTS algorithm for ADER-DG is very general and does not need any temporal synchronization between the elements, and is computationally much more efficient for problems with strongly varying element size or material parameters since it allows to reduce the total number of element updates considerably.

Multirate Timestepping Methods for Hyperbolic Conservation Laws

The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions.

Space–time adaptive numerical methods for geophysical applications

  • C. CastroM. KäserE. Toro
  • Computer Science
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2009
In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space–time adaptation technique using

Large-scale computations in fluid mechanics

Part 1: Semi-Lagrangian advective schemes and their use in meteorological modeling by J. R. Bates Adaptive mesh refinement for hyperbolic equations by M. J. Berger Averaged multivalued solutions and

A Discontinuous Galerkin Scheme Based on a Space–Time Expansion. I. Inviscid Compressible Flow in One Space Dimension

An explicit discontinuous Galerkin scheme for conservation laws which is of arbitrary order of accuracy in space and time for transient calculations and which drops the common global time levels and proposes that every grid zone runs with its own time step determined by the local stability restriction.