A truly forward semi-Lagrangian WENO scheme for the Vlasov-Poisson system

Sirajuddin, David; Hitchon, W. N. G.

doi:10.1016/j.jcp.2019.04.054

Cited by 10 publications

(7 citation statements)

References 115 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We remark that the limited schemes lead to an increase of the total energy error; this was indeed also already observed in [20]. Note that the results are kept in reasonable and comparable range as in the literature [44,45]. Lim behaves favorably w.r.t DaTe; SLWENO5 has the worst conservation.…”

Section: Strong Non Linear Landau Damping [20]supporting

confidence: 84%

“…Note that taking smaller CFL number leads generally to bigger error, as more interpolations are used, but only to a certain limit (as the interpolation gets more accurate when the foot of the characteristic approaches a grid point), which in fact corresponds to the Eulerian scheme (see e.g. [18]) where the time error becomes negligible (see [45] for a study where the number of interpolation is fixed and only the CFL number is changed). For the convergence study, we only consider the lim=Um+LC scheme and take different values of d, in order to see the influence of the degree.…”

Section: Free Transport Equationmentioning

confidence: 99%

“…In the sequel, we consider first two standard test cases: the strong non linear Landau damping and the two stream instability. We have not considered the linear Landau damping, but we expect better conservation error than in the strong non linear case (see for example [45]). Then, we consider the more challenging bump on tail test case, with three vortices.…”

Section: Vlasov-poisson Systemmentioning

confidence: 99%

“…We refer also to the recent paper [45] for some complementary references on the numerical resolution of the Vlasov equation by Semi-Lagrangian type methods focussing precisely on removing spurious oscillations, which is the concern of our paper.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Highly accurate monotonicity-preserving Semi-Lagrangian scheme for Vlasov-Poisson simulations

Yang

Mehrenberger

2021

Journal of Computational Physics

View full text Add to dashboard Cite

In this paper, we study a highly accurate monotonicity-preserving (MP) Semi-Lagrangian scheme for Vlasov-Poisson simulations. The classical Semi-Lagrangian scheme is known to be highly accurate and free from CFL condition, but it does not satisfy local maximum principle. To remedy this drawback, using the conservative form of the Semi-Lagrangian scheme, we recast existing MP schemes for the numerical flux in a common framework, and then substitute the local extremum by some "better" guess, in order to avoid as much as possible loss of accuracy and clipping near extrema, while keeping the monotonicity on monotone portions. With the limiter, on the one hand, the scheme keeps the good properties of the unlimited scheme: it is conservative, free from CFL condition and highly accurate. On the other hand, for locally monotonic data, the monotonicity of the solution is preserved. Numerical tests are made on free transport equation and Vlasov-Poisson system illustrating that the limited scheme is more diffusive compared to cubic splines but has better L 1 conservation, which is primarily an advantage for problems with sharp gradients.

show abstract

Section: Strong Non Linear Landau Damping [20]supporting

confidence: 84%

Section: Free Transport Equationmentioning

confidence: 99%

Section: Vlasov-poisson Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Highly accurate monotonicity-preserving Semi-Lagrangian scheme for Vlasov-Poisson simulations

Yang

Mehrenberger

2021

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…The SL scheme updates the solution by following the characteristics, either forwardly [10,25], or backwardly [19,14], where for (1) the characteristic equation is defined as dx dt = f (u(x, t)).…”

mentioning

confidence: 99%

A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations

Zhang

Zheng

Xiong

2021

era

View full text Add to dashboard Cite

In this paper, we propose a conservative semi-Lagrangian finite difference (SLFD) weighted essentially non-oscillatory (WENO) scheme, based on Runge-Kutta exponential integrator (RKEI) method, to solve one-dimensional scalar nonlinear hyperbolic equations. Conservative semi-Lagrangian schemes, under the finite difference framework, usually are designed only for linear or quasilinear conservative hyperbolic equations. Here we combine a conservative SLFD scheme developed in [21], with a high order RKEI method [7], to design conservative SLFD schemes, which can be applied to nonlinear hyperbolic equations. Our new approach will enjoy several good properties as the scheme for the linear or quasilinear case, such as, conservation, high order and large time steps. The new ingredient is that it can be applied to nonlinear hyperbolic equations, e.g., the Burgers' equation. Numerical tests will be performed to illustrate the effectiveness of our proposed schemes.

show abstract

Fourth-Order Conservative Non-splitting Semi-Lagrangian Hermite WENO Schemes for Kinetic and Fluid Simulations

Zheng,

Cai,

Qiu

et al. 2024

J Sci Comput

View full text Add to dashboard Cite

We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov–Poisson system, the guiding center Vlasov model, and the incompressible Euler equations in the vorticity-stream function formulation. The proposed SL HWENO schemes combine a weak formulation of the characteristic Galerkin method with two newly constructed HWENO reconstruction methods. The new HWENO reconstructions are meticulously designed to strike a delicate balance between curbing numerical oscillation and introducing excessive dissipation. Mass conservation naturally holds due to the weak formulation of the semi-Lagrangian discontinuous Galerkin method and the design of the HWENO reconstructions. We apply a positivity-preserving limiter to maintain the positivity of numerical solutions when needed. Abundant benchmark tests are performed to verify the effectiveness of the proposed SL HWENO schemes.

show abstract

A truly forward semi-Lagrangian WENO scheme for the Vlasov-Poisson system

Cited by 10 publications

References 115 publications

Highly accurate monotonicity-preserving Semi-Lagrangian scheme for Vlasov-Poisson simulations

Highly accurate monotonicity-preserving Semi-Lagrangian scheme for Vlasov-Poisson simulations

A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations

Fourth-Order Conservative Non-splitting Semi-Lagrangian Hermite WENO Schemes for Kinetic and Fluid Simulations

Contact Info

Product

Resources

About