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Comput."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the \u201csmall cut-cell\u201d problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge\u2013Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. The developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.<\/jats:p>","DOI":"10.1137\/22m1532019","type":"journal-article","created":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T04:59:35Z","timestamp":1695272375000},"page":"A2409-A2430","source":"Crossref","is-referenced-by-count":7,"title":["A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries"],"prefix":"10.1137","volume":"45","author":[{"given":"Nathaniel","family":"Overton-Katz","sequence":"first","affiliation":[{"name":"Lawrence Berkeley National Lab, Berkeley, CA, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinfeng","family":"Gao","sequence":"additional","affiliation":[{"name":"Colorado State University, Fort Collins, CO, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stephen","family":"Guzik","sequence":"additional","affiliation":[{"name":"Colorado State University, Fort Collins, CO, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oscar","family":"Antepara","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Lab, Berkeley, CA, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel T.","family":"Graves","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Lab, Berkeley, CA, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hans","family":"Johansen","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Lab, Berkeley, CA, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,9,21]]},"reference":[{"key":"ref1","unstructured":"M. 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