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Volume 14, Issue 4
Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow

Changsheng Yu, Tiegang Liu & Chengliang Feng

Adv. Appl. Math. Mech., 14 (2022), pp. 989-1016.

Published online: 2022-04

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  • Abstract

Heating or cooling one-dimensional inviscid compressible flow can be modeled by the Euler equations with energy sources. A tricky situation is the sudden appearance of a single-point energy source term. This source is discontinuous in both the time and space directions, and results in multiple discontinuous waves in the solution. We establish a mathematical model of the generalized Riemann problem of the Euler equations with source term. Based on the double CRPs coupling method proposed by the authors, we determine the wave patterns of the solution. Theoretically, we prove the existence and uniqueness of solutions to both "heat removal" problem and "heat addition" problem. Our results provide a theoretical explanation for the effect of instantaneous addition or removal of heat on the fluid.

  • AMS Subject Headings

35L81, 80A20

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COPYRIGHT: © Global Science Press

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@Article{AAMM-14-989, author = {}, title = {Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {4}, pages = {989--1016}, abstract = {

Heating or cooling one-dimensional inviscid compressible flow can be modeled by the Euler equations with energy sources. A tricky situation is the sudden appearance of a single-point energy source term. This source is discontinuous in both the time and space directions, and results in multiple discontinuous waves in the solution. We establish a mathematical model of the generalized Riemann problem of the Euler equations with source term. Based on the double CRPs coupling method proposed by the authors, we determine the wave patterns of the solution. Theoretically, we prove the existence and uniqueness of solutions to both "heat removal" problem and "heat addition" problem. Our results provide a theoretical explanation for the effect of instantaneous addition or removal of heat on the fluid.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0124}, url = {http://global-sci.org/intro/article_detail/aamm/20443.html} }
TY - JOUR T1 - Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 989 EP - 1016 PY - 2022 DA - 2022/04 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0124 UR - https://global-sci.org/intro/article_detail/aamm/20443.html KW - Hyperbolic balance law, generalized Riemann problem, singular source, existence and uniqueness. AB -

Heating or cooling one-dimensional inviscid compressible flow can be modeled by the Euler equations with energy sources. A tricky situation is the sudden appearance of a single-point energy source term. This source is discontinuous in both the time and space directions, and results in multiple discontinuous waves in the solution. We establish a mathematical model of the generalized Riemann problem of the Euler equations with source term. Based on the double CRPs coupling method proposed by the authors, we determine the wave patterns of the solution. Theoretically, we prove the existence and uniqueness of solutions to both "heat removal" problem and "heat addition" problem. Our results provide a theoretical explanation for the effect of instantaneous addition or removal of heat on the fluid.

Changsheng Yu, Tiegang Liu & Chengliang Feng. (2022). Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow. Advances in Applied Mathematics and Mechanics. 14 (4). 989-1016. doi:10.4208/aamm.OA-2021-0124
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