https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Markert_Gassner_2022aMarkert Gassner 2022a - Revision history2026-04-22T17:37:03ZRevision history for this page on the wikiMediaWiki 1.27.0-wmf.10https://www.scipedia.com/wd/index.php?title=Markert_Gassner_2022a&diff=262658&oldid=prevMove page script: Move page script moved page Markert Gassner 1970a to Markert Gassner 2022a2022-11-25T15:06:28Z<p>Move page script moved page <a href="/public/Markert_Gassner_1970a" class="mw-redirect" title="Markert Gassner 1970a">Markert Gassner 1970a</a> to <a href="/public/Markert_Gassner_2022a" title="Markert Gassner 2022a">Markert Gassner 2022a</a></p>
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</td></tr></table>Move page scripthttps://www.scipedia.com/wd/index.php?title=Markert_Gassner_2022a&diff=260762&oldid=prevJSanchez: JSanchez moved page Draft Sanchez Pinedo 233096299 to Markert Gassner 1970a2022-11-22T15:27:34Z<p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_233096299" class="mw-redirect" title="Draft Sanchez Pinedo 233096299">Draft Sanchez Pinedo 233096299</a> to <a href="/public/Markert_Gassner_1970a" class="mw-redirect" title="Markert Gassner 1970a">Markert Gassner 1970a</a></p>
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</td></tr></table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Markert_Gassner_2022a&diff=260761&oldid=prevJSanchez at 15:27, 22 November 20222022-11-22T15:27:29Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:27, 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;"><div>== Abstract ==</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>== Abstract ==</div></td></tr>
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</table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Markert_Gassner_2022a&diff=260759&oldid=prevJSanchez at 15:27, 22 November 20222022-11-22T15:27:27Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:27, 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>We review and compare two techniques to get entropy stability for nodal Discontinuous Galerkin Spectral Element Methods (DG) in compressible flows. One technique is based on entropy split-forms, e.g., [8, 15, 5] and one is based on a direct algebraic correction [1]. We have implemented the Flux Differencing methodology for both, Legendre-Gauss-Lobatto (Lobatto) and Legendre-Gauss (Gauss) based spectral element basis functions. While the Lobatto operators belong to the class of diagonal norm summation-by-parts (SBP) operators, the Gauss operators belong to the generalized class of SBP operators, where it is not necessary that the boundary nodes are included. To reach entropy stability, respectively guaranteed entropy dissipation, a key ingredient is an entropy conserving numerical flux function. With this ingredient, only the volume integral term of the DG method has to be modified accordingly. We have also implemented an alternative technique, which is in general applicable for a wide range of discretizations. Abgrall [R. Abgrall, A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes. Journal of Computational Physics, vol 372, 2018] introduced an algebraic correction term that retains conservation of the primary quantities and is furthermore constructed such, that an entropy (in-) equality can be shown. The second technique is at first sight a simpler alternative to the split-form based approach. Hence, questions regarding its advantages and disadvantages naturally come up.</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>We review and compare two techniques to get entropy stability for nodal Discontinuous Galerkin Spectral Element Methods (DG) in compressible flows. One technique is based on entropy split-forms, e.g., [8, 15, 5] and one is based on a direct algebraic correction [1]. We have implemented the Flux Differencing methodology for both, Legendre-Gauss-Lobatto (Lobatto) and Legendre-Gauss (Gauss) based spectral element basis functions. While the Lobatto operators belong to the class of diagonal norm summation-by-parts (SBP) operators, the Gauss operators belong to the generalized class of SBP operators, where it is not necessary that the boundary nodes are included. To reach entropy stability, respectively guaranteed entropy dissipation, a key ingredient is an entropy conserving numerical flux function. With this ingredient, only the volume integral term of the DG method has to be modified accordingly. We have also implemented an alternative technique, which is in general applicable for a wide range of discretizations. Abgrall [R. Abgrall, A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes. Journal of Computational Physics, vol 372, 2018] introduced an algebraic correction term that retains conservation of the primary quantities and is furthermore constructed such, that an entropy (in-) equality can be shown. The second technique is at first sight a simpler alternative to the split-form based approach. Hence, questions regarding its advantages and disadvantages naturally come up.</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=Markert_Gassner_2022a&diff=260757&oldid=prevJSanchez at 15:27, 22 November 20222022-11-22T15:27:25Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:27, 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;">We review and compare two techniques to get entropy stability for nodal Discontinuous Galerkin Spectral Element Methods (DG) in compressible flows. One technique is based on entropy split-forms, e.g., [8, 15, 5] and one is based on a direct algebraic correction [1]. We have implemented the Flux Differencing methodology for both, Legendre-Gauss-Lobatto (Lobatto) and Legendre-Gauss (Gauss) based spectral element basis functions. While the Lobatto operators belong to the class of diagonal norm summation-by-parts (SBP) operators, the Gauss operators belong to the generalized class of SBP operators, where it is not necessary that the boundary nodes are included. To reach entropy stability, respectively guaranteed entropy dissipation, a key ingredient is an entropy conserving numerical flux function. With this ingredient, only the volume integral term of the DG method has to be modified accordingly. We have also implemented an alternative technique, which is in general applicable for a wide range of discretizations. Abgrall [R. Abgrall, A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes. Journal of Computational Physics, vol 372, 2018] introduced an algebraic correction term that retains conservation of the primary quantities and is furthermore constructed such, that an entropy (in-) equality can be shown. The second technique is at first sight a simpler alternative to the split-form based approach. Hence, questions regarding its advantages and disadvantages naturally come up.</ins></div></td></tr>
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