https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=De_Michele_Coppola_2022aDe Michele Coppola 2022a - Revision history2026-04-25T18:35:45ZRevision history for this page on the wikiMediaWiki 1.27.0-wmf.10https://www.scipedia.com/wd/index.php?title=De_Michele_Coppola_2022a&diff=262804&oldid=prevMove page script: Move page script moved page De Michele Coppola 1970a to De Michele Coppola 2022a2022-11-25T15:06:39Z<p>Move page script moved page <a href="/public/De_Michele_Coppola_1970a" class="mw-redirect" title="De Michele Coppola 1970a">De Michele Coppola 1970a</a> to <a href="/public/De_Michele_Coppola_2022a" title="De Michele Coppola 2022a">De Michele Coppola 2022a</a></p>
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</td></tr></table>Move page scripthttps://www.scipedia.com/wd/index.php?title=De_Michele_Coppola_2022a&diff=260448&oldid=prevJSanchez: JSanchez moved page Draft Sanchez Pinedo 237766363 to De Michele Coppola 1970a2022-11-22T14:20:14Z<p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_237766363" class="mw-redirect" title="Draft Sanchez Pinedo 237766363">Draft Sanchez Pinedo 237766363</a> to <a href="/public/De_Michele_Coppola_1970a" class="mw-redirect" title="De Michele Coppola 1970a">De Michele Coppola 1970a</a></p>
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</td></tr></table>JSanchezhttps://www.scipedia.com/wd/index.php?title=De_Michele_Coppola_2022a&diff=260447&oldid=prevJSanchez at 14:20, 22 November 20222022-11-22T14:20:09Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 14:20, 22 November 2022</td>
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</table>JSanchezhttps://www.scipedia.com/wd/index.php?title=De_Michele_Coppola_2022a&diff=260445&oldid=prevJSanchez at 14:20, 22 November 20222022-11-22T14:20:07Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 14:20, 22 November 2022</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Nonlinear instabilities are one of the major problems in turbulence simulations. One reason behind this problem is the accumulation of aliasing errors produced by the discrete evaluation of the convective term. This can be improved by preserving the quadratic invariants in a discrete sense. However, another source of instabilities is the error due to an incorrect evolution of thermodynamic variables, such as entropy. An appropriate discretization of the energy equation is needed to address this issue. An analysis of the preservation properties of various discretizations of the compressible Euler equations is reported, which includes some of the most common approaches used in the literature, together with some new formulations. Two main factors have been identified and studied: one is the choice of the energy equation to be directly discretized; the other is the particular splitting of the convective terms, chosen among the Kinetic Energy Preserving (KEP) forms. The energy equations analyzed in this paper are total and internal energy, entropy, and speed of sound. All the cases examined are locally conservative and KEP, since this is considered an essential condition for a robust simulation. The differences among the formulations have been theoretically investigated through the study of the discrete evolution equations induced by the chosen energy variable, showing which quantities may be preserved. Both one-dimensional and two-dimensional tests have been performed to assess the advantages and disadvantages of the various options in different cases.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Nonlinear instabilities are one of the major problems in turbulence simulations. One reason behind this problem is the accumulation of aliasing errors produced by the discrete evaluation of the convective term. This can be improved by preserving the quadratic invariants in a discrete sense. However, another source of instabilities is the error due to an incorrect evolution of thermodynamic variables, such as entropy. An appropriate discretization of the energy equation is needed to address this issue. An analysis of the preservation properties of various discretizations of the compressible Euler equations is reported, which includes some of the most common approaches used in the literature, together with some new formulations. Two main factors have been identified and studied: one is the choice of the energy equation to be directly discretized; the other is the particular splitting of the convective terms, chosen among the Kinetic Energy Preserving (KEP) forms. The energy equations analyzed in this paper are total and internal energy, entropy, and speed of sound. All the cases examined are locally conservative and KEP, since this is considered an essential condition for a robust simulation. The differences among the formulations have been theoretically investigated through the study of the discrete evolution equations induced by the chosen energy variable, showing which quantities may be preserved. Both one-dimensional and two-dimensional tests have been performed to assess the advantages and disadvantages of the various options in different cases.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
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</table>JSanchezhttps://www.scipedia.com/wd/index.php?title=De_Michele_Coppola_2022a&diff=260443&oldid=prevJSanchez at 14:20, 22 November 20222022-11-22T14:20:06Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 14:20, 22 November 2022</td>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">                                </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Summary==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Nonlinear instabilities are one of the major problems in turbulence simulations. One reason behind this problem is the accumulation of aliasing errors produced by the discrete evaluation of the convective term. This can be improved by preserving the quadratic invariants in a discrete sense. However, another source of instabilities is the error due to an incorrect evolution of thermodynamic variables, such as entropy. An appropriate discretization of the energy equation is needed to address this issue. An analysis of the preservation properties of various discretizations of the compressible Euler equations is reported, which includes some of the most common approaches used in the literature, together with some new formulations. Two main factors have been identified and studied: one is the choice of the energy equation to be directly discretized; the other is the particular splitting of the convective terms, chosen among the Kinetic Energy Preserving (KEP) forms. The energy equations analyzed in this paper are total and internal energy, entropy, and speed of sound. All the cases examined are locally conservative and KEP, since this is considered an essential condition for a robust simulation. The differences among the formulations have been theoretically investigated through the study of the discrete evolution equations induced by the chosen energy variable, showing which quantities may be preserved. Both one-dimensional and two-dimensional tests have been performed to assess the advantages and disadvantages of the various options in different cases.</ins></div></td></tr>
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