000145650 001__ 145650 000145650 005__ 20241125101203.0 000145650 0247_ $$2doi$$a10.1016/j.compfluid.2023.105869 000145650 0248_ $$2sideral$$a140461 000145650 037__ $$aART-2023-140461 000145650 041__ $$aeng 000145650 100__ $$0(orcid)0000-0003-3570-0202$$aLlorente, Victor J. 000145650 245__ $$aA modified equation analysis for immersed boundary methods based on volume penalization: Applications to linear advection–diffusion equations and high-order discontinuous Galerkin schemes 000145650 260__ $$c2023 000145650 5060_ $$aAccess copy available to the general public$$fUnrestricted 000145650 5203_ $$aThe Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with high-order methods (e.g., discontinuous Galerkin). For this combination to be effective, an analysis of the numerical errors is essential. In this work, we apply, for the first time, a modified equation analysis to the combination of IBM (based on volume penalization) and high-order methods (based on nodal discontinuous Galerkin methods) to analyze a priori numerical errors and obtain practical guidelines on the selection of IBM parameters. The analysis is performed on a linear advection–diffusion equation with Dirichlet boundary conditions. Three ways to penalize the immersed boundary are considered, the first penalizes the solution inside the IBM region (classic approach), whilst the second and third penalize the first and second derivatives of the solution. We find optimal combinations of the penalization parameters, including the first and second penalizing derivatives, resulting in minimum errors. We validate the theoretical analysis with numerical experiments for one- and two-dimensional advection–diffusion equations 000145650 536__ $$9info:eu-repo/grantAgreement/EC/H2020/813605/EU/813605/ASIMIA$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 813605-ASIMIA$$9info:eu-repo/grantAgreement/EC/H2020/956104/EU/CODA: Next generation of industrial aerodynamic simulation code/NextSim$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 956104-NextSim$$9info:eu-repo/grantAgreement/ES/MICINN AEI/EIN2020-112315 000145650 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000145650 590__ $$a2.5$$b2023 000145650 591__ $$aMECHANICS$$b71 / 170 = 0.418$$c2023$$dQ2$$eT2 000145650 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b88 / 170 = 0.518$$c2023$$dQ3$$eT2 000145650 592__ $$a0.885$$b2023 000145650 593__ $$aComputer Science (miscellaneous)$$c2023$$dQ1 000145650 593__ $$aEngineering (miscellaneous)$$c2023$$dQ1 000145650 594__ $$a5.3$$b2023 000145650 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000145650 700__ $$aKou, Jiaqing 000145650 700__ $$aValero, Eusebio 000145650 700__ $$aFerrer, Esteban 000145650 773__ $$g257 (2023), 105869 [16 pp.]$$pComput. fluids$$tComputers and Fluids$$x0045-7930 000145650 8564_ $$s2598548$$uhttps://zaguan.unizar.es/record/145650/files/texto_completo.pdf$$yVersión publicada 000145650 8564_ $$s2687768$$uhttps://zaguan.unizar.es/record/145650/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000145650 909CO $$ooai:zaguan.unizar.es:145650$$particulos$$pdriver 000145650 951__ $$a2024-11-22-12:13:00 000145650 980__ $$aARTICLE