國立虎尾科技大學 |

A Nonlinear Conservation Law Modeling Carbon Sequestration.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	A Nonlinear Conservation Law Modeling Carbon Sequestration./
作者:	Brown, Elisabeth Mary Margaret.
面頁冊數:	1 online resource (138 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
標題:	Applied mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9781369855623

A Nonlinear Conservation Law Modeling Carbon Sequestration.
Brown, Elisabeth Mary Margaret.

A Nonlinear Conservation Law Modeling Carbon Sequestration. - 1 online resource (138 pages)

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide (CO2) migration and storage through residual trapping [17]. Dual flux curves emerge in this model, giving rise to flux discontinuities. One flux describes the invasion of the plume into pore space, and the other captures the flow as the plume drains and leaves CO2 bubbles behind, which are then trapped by brine in the pore space between rock grains. Flux functions with discontinuities in space have been previously studied; however, the flux in this model depends on how the plume height changes in time, a different kind of discontinuity that introduces new patterns. A striking feature of this simple model is that, because of its dual flux curves, solutions of the conservation law can include the prediction that the entire CO2 plume is deposited as bubbles in a finite time.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369855623Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

A Nonlinear Conservation Law Modeling Carbon Sequestration.
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100 1 $a Brown, Elisabeth Mary Margaret. $3 1182495
245 1 2 $a A Nonlinear Conservation Law Modeling Carbon Sequestration.
264 0 $c 2017
300 $a 1 online resource (138 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
502 $a Thesis (Ph.D.) $c North Carolina State University $d 2017.
504 $a Includes bibliographical references
520 $a A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide (CO2) migration and storage through residual trapping [17]. Dual flux curves emerge in this model, giving rise to flux discontinuities. One flux describes the invasion of the plume into pore space, and the other captures the flow as the plume drains and leaves CO2 bubbles behind, which are then trapped by brine in the pore space between rock grains. Flux functions with discontinuities in space have been previously studied; however, the flux in this model depends on how the plume height changes in time, a different kind of discontinuity that introduces new patterns. A striking feature of this simple model is that, because of its dual flux curves, solutions of the conservation law can include the prediction that the entire CO2 plume is deposited as bubbles in a finite time.
520 $a The model is explored in more detail, and some mathematical issues are resolved. We describe the construction of fundamental wave solutions of the equation, namely shock waves and rarefaction fans. To establish the admissibility of shock waves, we introduce the notion of cross-hatch characteristics to address the ambiguity of characteristic speeds in regions of the characteristic plane where the solution is constant. Detailed analytic solutions of wave interactions resulting from the dual flux model include some properties that do not occur in conventional scalar conservation laws. Some wave interactions yield novel phenomena due to the dual flux, such as shock-rarefaction interactions that would persist for all time with a single flux, here are completed in finite time.
520 $a The existence of an entropy solution of the Cauchy problem for any initial CO2 plume is established using wave-front tracking. To prove this theorem, we construct piecewise constant approximate solutions of the Cauchy problem using expansion shocks in place of rarefaction waves. In order to establish that a subsequence of approximate solutions converges to an entropy solution of the Cauchy problem, we have to account for the dual fluxes carefully.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a North Carolina State University. $b Applied Mathematics. $3 1180809
773 0 $t Dissertation Abstracts International $g 78-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10610679 $z click for full text (PQDT)