High Order Numerical Simulations for the Binary Fluid--Surfactant System Using the Discontinuous Galerkin and Spectral Deferred Correction Methods

2020 ◽  
Vol 42 (2) ◽  
pp. B353-B378
Author(s):  
Ruihan Guo ◽  
Yan Xu
Keyword(s):  
Numerical Simulations ◽  
Discontinuous Galerkin ◽  
High Order ◽  
Binary Fluid ◽  
Deferred Correction ◽  
Surfactant System ◽  
Spectral Deferred Correction

scholarly journals A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry

2016 ◽  
Vol 20 (3) ◽  
pp. 521-547 ◽  
Author(s):  
Will E. Pazner ◽  
Andrew Nonaka ◽  
John B. Bell ◽  
Marcus S. Day ◽  
Michael L. Minion
Keyword(s):  
Mach Number ◽  
High Order ◽  
Low Mach Number ◽  
Deferred Correction ◽  
Number Flow ◽  
Complex Chemistry ◽  
Spectral Deferred Correction ◽  
Low Mach Number Flow

scholarly journals High-order partitioned spectral deferred correction solvers for multiphysics problems

2020 ◽  
Vol 412 ◽  
pp. 109441 ◽  
Author(s):  
Daniel Z. Huang ◽  
Will Pazner ◽  
Per-Olof Persson ◽  
Matthew J. Zahr
Keyword(s):  
High Order ◽  
Deferred Correction ◽  
Spectral Deferred Correction ◽  
Multiphysics Problems

A Spectral Deferred Correction Method Applied to the Shallow Water Equations on a Sphere

2013 ◽  
Vol 141 (10) ◽  
pp. 3435-3449 ◽  
Author(s):  
Jun Jia ◽  
Judith C. Hill ◽  
Katherine J. Evans ◽  
George I. Fann ◽  
Mark A. Taylor
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Correction Method ◽  
Higher Order ◽  
High Order ◽  
Benchmark Problems ◽  
Time Step ◽  
Deferred Correction ◽  
Long Time ◽  
Spectral Deferred Correction

Abstract Although significant gains have been made in achieving high-order spatial accuracy in global climate modeling, less attention has been given to the impact imposed by low-order temporal discretizations. For long-time simulations, the error accumulation can be significant, indicating a need for higher-order temporal accuracy. A spectral deferred correction (SDC) method is demonstrated of even order, with second- to eighth-order accuracy and A-stability for the temporal discretization of the shallow water equations within the spectral-element High-Order Methods Modeling Environment (HOMME). Because this method is stable and of high order, larger time-step sizes can be taken while still yielding accurate long-time simulations. The spectral deferred correction method has been tested on a suite of popular benchmark problems for the shallow water equations, and when compared to the explicit leapfrog, five-stage Runge–Kutta, and fully implicit (FI) second-order backward differentiation formula (BDF2) time-integration methods, it achieves higher accuracy for the same or larger time-step sizes. One of the benchmark problems, the linear advection of a Gaussian bell height anomaly, is extended to run for longer time periods to mimic climate-length simulations, and the leapfrog integration method exhibited visible degradation for climate length simulations whereas the second-order and higher methods did not. When integrated with higher-order SDC methods, a suite of shallow water test problems is able to replicate the test with better accuracy.

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