Citation: Frederike Kissling, Christian Rohde. The computation of nonclassical shock waves with a heterogeneousmultiscale method[J]. Networks and Heterogeneous Media, 2010, 5(3): 661-674. doi: 10.3934/nhm.2010.5.661
[1] | Frederike Kissling, Christian Rohde . The computation of nonclassical shock waves with a heterogeneous multiscale method. Networks and Heterogeneous Media, 2010, 5(3): 661-674. doi: 10.3934/nhm.2010.5.661 |
[2] | Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra . Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks and Heterogeneous Media, 2013, 8(4): 969-984. doi: 10.3934/nhm.2013.8.969 |
[3] | Clément Cancès . On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types. Networks and Heterogeneous Media, 2010, 5(3): 635-647. doi: 10.3934/nhm.2010.5.635 |
[4] | Laura Caravenna, Laura V. Spinolo . New interaction estimates for the Baiti-Jenssen system. Networks and Heterogeneous Media, 2016, 11(2): 263-280. doi: 10.3934/nhm.2016.11.263 |
[5] | Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski . An improved homogenization result for immiscible compressible two-phase flow in porous media. Networks and Heterogeneous Media, 2017, 12(1): 147-171. doi: 10.3934/nhm.2017006 |
[6] | Francesca Marcellini . Existence of solutions to a boundary value problem for a phase transition traffic model. Networks and Heterogeneous Media, 2017, 12(2): 259-275. doi: 10.3934/nhm.2017011 |
[7] | Wen-Ching Lien, Yu-Yu Liu, Chen-Chang Peng . Smooth Transonic Flows Around Cones. Networks and Heterogeneous Media, 2022, 17(6): 827-845. doi: 10.3934/nhm.2022028 |
[8] | Maya Briani, Benedetto Piccoli . Fluvial to torrential phase transition in open canals. Networks and Heterogeneous Media, 2018, 13(4): 663-690. doi: 10.3934/nhm.2018030 |
[9] | Mario Ohlberger, Ben Schweizer, Maik Urban, Barbara Verfürth . Mathematical analysis of transmission properties of electromagnetic meta-materials. Networks and Heterogeneous Media, 2020, 15(1): 29-56. doi: 10.3934/nhm.2020002 |
[10] | Raimund Bürger, Stefan Diehl, M. Carmen Martí, Yolanda Vásquez . A difference scheme for a triangular system of conservation laws with discontinuous flux modeling three-phase flows. Networks and Heterogeneous Media, 2023, 18(1): 140-190. doi: 10.3934/nhm.2023006 |
1. | D. Wirtz, N. Karajan, B. Haasdonk, Surrogate modeling of multiscale models using kernel methods, 2015, 101, 00295981, 1, 10.1002/nme.4767 | |
2. | Gaurav Goel, Luqman K. Abidoye, Bhagu R. Chahar, Diganta B. Das, Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect, 2016, 16, 1567-7419, 945, 10.1007/s10652-016-9459-y | |
3. | Qiang Du, James R. Kamm, R. B. Lehoucq, Michael L. Parks, A New Approach for a Nonlocal, Nonlinear Conservation Law, 2012, 72, 0036-1399, 464, 10.1137/110833233 | |
4. | Ch. Chalons, P. Engel, Ch. Rohde, A Conservative and Convergent Scheme for Undercompressive Shock Waves, 2014, 52, 0036-1429, 554, 10.1137/120897821 | |
5. | Christian Rohde, Christoph Zeiler, A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension, 2015, 95, 01689274, 267, 10.1016/j.apnum.2014.05.001 | |
6. | Frederike Kissling, Christian Rohde, The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case, 2015, 13, 1540-3459, 1507, 10.1137/120899236 | |
7. | Luqman K. Abidoye, Diganta B. Das, Scale dependent dynamic capillary pressure effect for two-phase flow in porous media, 2014, 74, 03091708, 212, 10.1016/j.advwatres.2014.09.009 | |
8. | Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra, Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes, 2013, 8, 1556-181X, 969, 10.3934/nhm.2013.8.969 | |
9. | Hélène Mathis, Clément Cancès, Edwige Godlewski, Nicolas Seguin, Dynamic Model Adaptation for Multiscale Simulation of Hyperbolic Systems with Relaxation, 2015, 63, 0885-7474, 820, 10.1007/s10915-014-9915-0 | |
10. | Philippe G. LeFloch, Siddhartha Mishra, Numerical methods with controlled dissipation for small-scale dependent shocks, 2014, 23, 0962-4929, 743, 10.1017/S0962492914000099 | |
11. | Frederike Kissling, Rainer Helmig, Christian Rohde, Simulation of Infiltration Processes in the Unsaturated Zone Using a Multiscale Approach, 2012, 11, 15391663, vzj2011.0193, 10.2136/vzj2011.0193 | |
12. | Y. Cao, R. Helmig, B. Wohlmuth, A two-scale operator-splitting method for two-phase flow in porous media, 2011, 34, 03091708, 1581, 10.1016/j.advwatres.2011.07.002 | |
13. |
M. Ndjinga, T. P. K. Nguyen, C. Chalons,
A hyperbolic system modelling incompressible two phase flows: theory and numerics,
2017,
24,
1021-9722,
10.1007/s00030-017-0458-6
|
|
14. | Qiang Du, Zhan Huang, Philippe G. LeFloch, Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models, 2017, 55, 0036-1429, 2465, 10.1137/16M1105372 | |
15. | Stefan Karpinski, Iuliu Sorin Pop, Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects, 2017, 136, 0029-599X, 249, 10.1007/s00211-016-0839-5 |