Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

1
14
1

Year Published

2015
2015
2019
2019

Publication Types

Select...
4

Relationship

0
4

Authors

Journals

citations
Cited by 10 publications
references
References 18 publications
1
14
1
Order By: Relevance
“…A key issue in the MMPDE method is choosing an appropriate monitor function, so that its adaptive re-meshing process effectively works. For resolving shock waves in hyperbolic conservation laws 18) , the so-called arc-type monitor functions were proposed and successfully applied to a variety of test and real cases, ranging from the inviscid Burgers-type equations 19) to the relativistic fluid dynamical equations governing evolution of galaxy 20) . Another key issue in the MMPDE method is conservation property, which is one of the most important mathematical and physical properties equipped with the conservation laws, such as the KFEs and governing equations of hydrodynamics 21) .…”
Section: (2) Mmpde Methods A) Outline Of the Mmpde Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…A key issue in the MMPDE method is choosing an appropriate monitor function, so that its adaptive re-meshing process effectively works. For resolving shock waves in hyperbolic conservation laws 18) , the so-called arc-type monitor functions were proposed and successfully applied to a variety of test and real cases, ranging from the inviscid Burgers-type equations 19) to the relativistic fluid dynamical equations governing evolution of galaxy 20) . Another key issue in the MMPDE method is conservation property, which is one of the most important mathematical and physical properties equipped with the conservation laws, such as the KFEs and governing equations of hydrodynamics 21) .…”
Section: (2) Mmpde Methods A) Outline Of the Mmpde Methodsmentioning
confidence: 99%
“…Assembling Eq. (19) for every i with the abovepresented numerical fluxes leads to a linear system of ordinary differential equations (ODEs) that governs temporal evolution of the nodal solutions i w , which is subject to an appropriate initial condition at the initial time in this paper. Temporal integration of the system of ODEs can be performed with an available numerical method.…”
Section: (1) Dfv Scheme With Fitting Techniquementioning
confidence: 99%
“…We choose these problems as our test examples because they have been used extensively in the adaptive methods literature. It is worth emphasizing that these problems are also the ones used in [6,9,29,30,33].…”
Section: Methodsmentioning
confidence: 99%
“…Budd et al in [7] applied mesh movement. Soheili et al used a moving-mesh PDE (MMPDE) approach [8]. In [9], Ramadan et al suggested a method based on collocation of septic B-splines over finite elements for numerical solutions of the non-linear Burgers equation.…”
Section: Introductionmentioning
confidence: 99%