相关论文: Implicit shock tracking for unsteady flows by the …
High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the computational mesh with non-smooth features to represent them…
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…
A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuous Galerkin (DG) discretization was introduced in [38].…
This work introduces an optimization-based $rp$-adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order discontinuous Galerkin discretization on traditionally…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
We present a high order, robust, and stable shock-capturing technique for finite element approximations of ideal MHD. The method uses continuous Lagrange polynomials in space and explicit Runge-Kutta schemes in time. The shock-capturing…
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume…
We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The…
The paper aims at developing low-storage implicit Runge-Kutta methods which are easy to implement and achieve higher-order of convergence for both the velocity and pressure in the finite volume formulation of the incompressible…
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…
We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions to stochastic differential equations driven by processes that are rougher than a Brownian motion. We use a Taylor series representation…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
A mixed accuracy framework for Runge--Kutta methods presented in Grant [JSC 2022] and applied to diagonally implicit Runge--Kutta (DIRK) methods can significantly speed up the computation by replacing the implicit solver by less expensive…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…