Acceleration on stretched meshes with line-implicit LU-SGS in parallel implementation

Otero, Evelyn; Eliasson, Peter

doi:10.1080/10618562.2015.1021692

Cited by 9 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Linear-implicit scheme allows to make large time steps, with small quantity of exchanges between the blocks. Stability and efficiency of such linear-implicit schemes have been studied in literature, and there are examples of successful application of linear-implicit schemes to difficult practical tasks [25]. Another way to improve the calculation efficiency is the "in-flight" construction of a database to solve the equations of kinetics.…”

Section: -3mentioning

confidence: 99%

Simulation of flow development in high-speed combustor in 2D and 3D formulations

Власенко¹,

Matyash²,

Molev³

et al. 2018

AIP Conference Proceedings

View full text Add to dashboard Cite

Model high-speed combustor on gaseous hydrocarbon fuel, prepared for experiments in T-131 wind tunnel of TsAGI, is presented. Experiments are projected to create an experimental database for validation of calculations and physical models of turbulence and combustion. Geometry of combustor and prepared measurements are described. The main subject of paper is preliminary calculations of this combustor. Numerical methods for 2D and 3D URANS calculations are described. Special attention is given to numerical techniques allowing fast calculations of 3D unsteady flow development in the combustor. Approach to parallel realization of Fractional Time Stepping (FTS) technology is described. One way of In Situ Adaptive Tabulation (ISAT) of kinetic equations solution during the calculation is presented. Possible gasdynamic structure of flow in the combustor with the flame stabilization both in subsonic and in supersonic regime is described. Asymmetrical stationary solution (for the symmetrically-expanding duct) and symmetrical solution with flame oscillations are found and analyzed.

show abstract

Section: -3mentioning

confidence: 99%

Simulation of flow development in high-speed combustor in 2D and 3D formulations

Власенко¹,

Matyash²,

Molev³

et al. 2018

AIP Conference Proceedings

View full text Add to dashboard Cite

show abstract

“…In the last decades, significant progress has been made in the development of implicit numerical algorithms for steady flow simulations. For example, the LU-SGS method (Yoon & Jameson 1988;Otero & Eliasson 2015a, 2015b, the GMRES algorithm with an LU-SGS preconditioner (Luo et al 1998), etc. What they have in common is that they cannot make full use of the compactness of DG methods which is favorable for massive parallel computations.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Solar Corona with an Implicit High-order Reconstructed Discontinuous Galerkin Scheme

Liu

Feng

Zhang

et al. 2023

ApJS

View full text Add to dashboard Cite

The present study aims to apply an implicit high-order reconstructed discontinuous Galerkin (DG) scheme (rDG(P 1 P 2)) to simulate the steady-state solar corona. In this scheme, a piecewise quadratic polynomial solution, P 2, is obtained from the underlying piecewise linear DG solution, P 1, by least-squares reconstruction with a weighted essentially nonoscillatory limiter. The reconstructed quadratic polynomial solution is then used for the computation of the fluxes and source terms. In addition, an implicit time integration method with large time steps is considered in this work. The resulting large linear algebraic system of equations from the implicit discretization is solved by the cellwise relaxation implicit scheme which can make full use of the compactness of the DG scheme. The code of the implicit high-order rDG scheme is developed in Fortran language with message passing interface parallelization in Cartesian coordinates. To validate this code, we first test a problem with an exact solution, which confirms the expected third-order accuracy. Then we simulate the solar corona for Carrington rotations 2167, 2183, and 2210, and compare the modeled results with observations. We find that the numerical results basically reproduce the large-scale observed structures of the solar corona, such as coronal holes, helmet streamers, pseudostreamers, and high- and low-speed streams, which demonstrates the capability of the developed scheme.

show abstract

“…Usually in the implicit format, the approximate linearization of the nonlinear residual term enables us to obtain a system of linear equations. For instance, the approximate Jacobian strategies were used to solve both the nonlinear Navier-Stokes equations (e.g., Jespersen & Pulliam 1983;Barth 1987;Xia et al 2014;Otero & Eliasson 2015a, 2015b, and the MHD problem of low plasma β (e.g., Feng et al 2021). Compared with the true linearization that is complex and can be undefined in some cases, the approximate linearizations are much less costly and also perform well at large CFL numbers (e.g., Jespersen & Pulliam 1983;Barth 1987;Xia et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Implicit Solar Coronal Magnetohydrodynamic (MHD) Modeling with a Low-dissipation Hybridized AUSM-HLL Riemann Solver

Wang

Xiang

Liu

et al. 2022

ApJ

View full text Add to dashboard Cite

In this paper, we develop a 3D implicit single-fluid magnetohydrodynamic (MHD) model to simulate the steady-state solar corona with a wide range of Mach numbers and low plasma β. We employ a low-dissipation advection upstream splitting method (AUSM) to calculate the convective flux in the regions of low Mach numbers for a high resolution, and hybridize the AUSM with Harten-Lax-van Leer Riemann solver in the regions of high Mach numbers to improve the solver’s robustness. The inner boundary condition of no backflow is implemented by numerical flux. A reconstruction method based on the divergence-free radial basis function is adopted to enhance the divergence-free constraint of magnetic field. Also, an anisotropic thermal conduction term is considered; the positivity-preserving reconstruction method is used to prevent the presence of negative thermal pressure and plasma density, and the implicit lower-upper symmetric Gauss Seidel method is implemented for a better convergence rate. After establishing the implicit solar wind MHD model, we employ it to simulate steady-state solar coronal structures in Carrington rotations 2177 and 2212. The simulations demonstrate that the MHD model’s computational efficiency is desirable, and the modeled results are basically in agreement with the solar coronal observations and the mapped in situ measurements from the OMNI archive. Consequently, this implicit MHD model is promising to simulate a complex plasma environment with high-intensity magnetic field and wide-ranging Mach numbers.

show abstract

Acceleration on stretched meshes with line-implicit LU-SGS in parallel implementation

Cited by 9 publications

References 39 publications

Simulation of flow development in high-speed combustor in 2D and 3D formulations

Simulation of flow development in high-speed combustor in 2D and 3D formulations

Modeling the Solar Corona with an Implicit High-order Reconstructed Discontinuous Galerkin Scheme

Implicit Solar Coronal Magnetohydrodynamic (MHD) Modeling with a Low-dissipation Hybridized AUSM-HLL Riemann Solver

Contact Info

Product

Resources

About