相关论文: Local Time-Stepping for the Shallow Water Equation…

We present the formulation and optimization of a Runge-Kutta-type time-stepping scheme for solving the shallow water equations, aimed at substantially increasing the effective allowable time-step over that of comparable methods. This…

Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…

An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally…

We assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LTS is to speed up the simulation by allowing different…

The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial…

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any…

The timestep of the Finite-Difference Time-Domain method (FDTD) is constrained by the stability limit known as the Courant-Friedrichs-Lewy (CFL) condition. This limit can make FDTD simulations quite time consuming for structures containing…

We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous…

This paper presents the first scientific application of local time-stepping (LTS) schemes in the Model for Prediction Across Scales-Ocean (MPAS-O). We use LTS schemes in a single-layer, global ocean model that predicts the storm surge…

There is a growing interest in investigating numerical approximations of the water wave equation in recent years, whereas the lack of rigorous analysis of its time discretization inhibits the design of more efficient algorithms. In this…

Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…

In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta…

Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for…

We design and analyse a semi-implicit finite volume scheme for the two-dimensional rotating shallow water (RSW) equations that is energy stable, well-balanced (capable of preserving discrete geostrophic steady states), consistent, and…

We present an iterative IMPES solver and a novel timestep criterion for the simulation of immiscible two-phase flow involving compressible fluid phases. The novel timestep criterion uses the Courant-Friedrichs-Lewy (CFL) condition and…

Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…

Direct and large-eddy simulations of turbulence are often solved using explicit temporal schemes. However, this imposes very small time-steps because the eigenvalues of the (linearized) dynamical system, re-scaled by the time-step, must lie…

A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…

Quantum computing shows substantial potential in accelerating simulations and alleviating memory bottlenecks in computational fluid dynamics (CFD), owing to its inherent properties of superposition and entanglement. The lattice Boltzmann…

New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit for the…