A conservative semi-Lagrangian HWENO method for the Vlasov equation

@article{Cai2016ACS,
  title={A conservative semi-Lagrangian HWENO method for the Vlasov equation},
  author={Xiaofeng Cai and Jianxian Qiu and Jing-Mei Qiu},
  journal={J. Comput. Phys.},
  year={2016},
  volume={323},
  pages={95-114}
}
In this paper, we propose a high order conservative semi-Lagrangian (SL) finite difference Hermite weighted essentially non-oscillatory (HWENO) method for the Vlasov equation based on dimensional splitting. HWENO was first proposed for solving nonlinear hyperbolic problems by evolving both function values and its first derivative values (Qiu and Shu (2004) 23). The major advantage of HWENO, compared with the original WENO, lies in its compactness in reconstruction stencils.There are several new… Expand
A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting
TLDR
A high order semi-Lagrangian discontinuous Galerkin (DG) method for nonlinear Vlasov–Poisson simulations without operator splitting that is locally mass conservative, free of splitting error, positivity-preserving, stable and robust for large time stepping size. Expand
High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation
  • A. Christlieb, Matthew Link, Hyoseon Yang, Ruimeng Chang
  • Computer Science
  • Communications on Applied Mathematics and Computation
  • 2021
TLDR
A semi-Lagrangian (SL) method based on a non-polynomial function space for solving the Vlasov equation is presented and a key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method. Expand
A truly forward semi-Lagrangian WENO scheme for the Vlasov-Poisson system
TLDR
A class of modular high order forward semi-Lagrangian schemes with a number of advantages for linear advection equations is extended to have high resolution, in the sense that sharp gradients can be captured without loss of accuracy, by means of weighted essentially non-oscillatory derivative calculations based on finite differences. Expand
A Generalized Eulerian-Lagrangian Discontinuous Galerkin Method for Transport Problems
TLDR
The newly proposed GEL DG method is motivated for solving linear hyperbolic systems with variable coefficients, where the velocity field for adjoint problems of the test functions is frozen to constant and the semi-discrete scheme over the space-time region partitioned by linear lines approximating characteristics is proposed. Expand
Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier-Stokes equations
TLDR
The positivity-preserving hybrid HWENO scheme in this paper is not only more efficient but also much more robust than the conventional HWENNO method for both compressible Euler and compressible Navier-Stokes equations, especially for solving gas dynamics equations in low density and low pressure regime. Expand
A Conservative Semi-Lagrangian Finite Volume Method for Convection-Diffusion Problems on Unstructured Grids
TLDR
A conservative semi-Lagrangian finite volume method is presented for the numerical solution of convection–diffusion problems on unstructured grids and the focus is on constructing efficient solvers with large stability regions and fully conservative to solve convection-dominated flow problems. Expand
A high order bound preserving finite difference linear scheme for incompressible flows
We propose a high order finite difference linear scheme combined with a high order bound preserving maximum-principle-preserving (MPP) flux limiter to solve the incompressible flow system. For suchExpand
Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations
TLDR
This paper makes a comparison between the splitting and non-splitting SLDG methods for multi-dimensional transport simulations and offers a practical guide for choosing optimal S LDG solvers for linear and nonlinear transport simulations. Expand
Shape-preserving and mass-conserving semi-Lagrangian approaches
TLDR
Different techniques that have been developed to ensure that the semi-Lagrangian scheme can preserve the shape of the body being advected are introduced to avoid the Gibbs phenomena of the under- and overshoots. Expand
Curriculum Vitae
Visiting scholar, University of California Los Angeles (UCLA) (August 1973-July 1974). Lecturer and Assistant Professor in Mathematics and Functional Analysis, University of Calabria (1974-1983).Expand
...
1
2
...

References

SHOWING 1-10 OF 41 REFERENCES
A conservative high order semi-Lagrangian WENO method for the Vlasov equation
TLDR
A novel Vlasov solver based on a semi-Lagrangian method which combines Strang splitting in time with high order WENO (weighted essentially non-oscillatory) reconstruction in space is proposed, suggesting the use of high order reconstruction is advantageous when considering the Vlasova-Poisson system. Expand
Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation
TLDR
A new conservative hybrid finite element-finite difference method for the Vlasov equation that enjoys great computational efficiency, as it allows one to use relatively coarse phase space mesh due to the high order nature of the scheme. Expand
Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation
In this paper, we propose a new conservative semi-Lagrangian (SL) finite difference (FD) WENO scheme for linear advection equations, which can serve as a base scheme for the Vlasov equation by StrangExpand
Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov-Poisson system
TLDR
A new Strang split SL discontinuous Galerkin (DG) method for solving the Vlasov equation is proposed and the recently developed positivity preserving (PP) limiter is applied to the scheme to ensure the positivity of the unknown probability density function without affecting the high order accuracy of the base SL DG scheme. Expand
A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes
In this paper, we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes based on the work (Computers & Fluids, 34: 642–663 (2005))Expand
Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow
TLDR
The proposed conservative semi-Lagrangian finite difference framework is coupled with high order essentially non-oscillatory (ENO or weighted ENO (WENO) reconstructions to achieve high order accuracy in smooth parts of the solution and to capture sharp interfaces without introducing spurious oscillations. Expand
Finite Difference Hermite WENO Schemes for Hyperbolic Conservation Laws
TLDR
A class of weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO), for solving one and two dimensional nonlinear hyperbolic conservation law systems is presented. Expand
High order maximum principle preserving semi-Lagrangian finite difference WENO schemes for the Vlasov equation
TLDR
The parametrized maximum principle preserving (MPP) flux limiter is proved to maintain up to fourth order accuracy for the semi-Lagrangian finite difference scheme without any time step restriction. Expand
Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one-dimensional case
In this paper, a class of fifth-order weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one-dimensional nonlinearExpand
A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
TLDR
This work develops a method that discretizes the 1+1 Vlasov-Poisson system via a high-order discontinuous Galerkin (DG) method in phase space, and an operator split, semi-Lagrangian method in time, and shows how to resolve all of the Lagrangian dynamics in such a way that mass is exactly conserved, positivity is maintained, and high- order accuracy is achieved. Expand
...
1
2
3
4
5
...