An investigation of random choice method for three-dimensional steady supersonic flows

Loh, Ching Y.; Liou, Meng-Sing; Hui, W. H.

doi:10.1002/(sici)1097-0363(19990115)29:1<97::aid-fld780>3.0.co;2-j

Cited by 3 publications

(1 citation statement)

References 29 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later it was used as a numerical tool by Chorin in gas dynamics [22,23]. Chorin's work was followed by numerous researchers, with applications and further improvements in [24][25][26], and more recently [27,28], etc. The main advantage of this method is the sharp resolutions of shocks and especially, contact discontinuities.…”

Section: Introductionmentioning

confidence: 99%

On the Quasi-Random Choice Method for the Liouville Equation of Geometrical Optics with Discontinuous Wave Speed

Jin²

2013

JCM

View full text Add to dashboard Cite

We study the quasi-random choice method (QRCM) for the Liouville equation of geometrical optics with discontinuous local wave speed. This equation arises in the phase space computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discontinuities, and measure-valued solutions. The so-called QRCM is a random choice method based on quasi-random sampling (a deterministic alternative to random sampling). The method not only is viscosity-free but also provides faster convergence rate. Therefore, it is appealing for the problem under study which is indeed a Hamiltonian flow. Our analysis and computational results show that the QRCM 1) is almost first-order accurate even with the aforementioned discontinuities; 2) gives sharp resolutions for all discontinuities encountered in the problem; and 3) for measure-valued solutions, does not need the level set decomposition for finite difference/volume methods with numerical viscosities.Mathematics subject classification: 35L45, 65M06, 11K45.

show abstract