{"product_id":"error-freed-cfd-mathematics-9783119147767","title":"Error Freed CFD Mathematics","description":"\u003cp\u003e\u003cem\u003eError Freed \u003c\/em\u003eCFD\u003cem\u003e Mathematics\u003c\/em\u003e analytically derives and validates \u003cem\u003enonlinear\u003c\/em\u003e continuum calculus \u003cem\u003ealterations\u003c\/em\u003e to Navier-Stokes partial differential equation systems that completely \u003cem\u003eannihilate \u003c\/em\u003ethe legacy CFD theory\/practice \u003cem\u003eintrinsic\u003c\/em\u003e error mechanisms\u003cem\u003e \u003c\/em\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003espatial-temporal discretization generated instability\u003c\/li\u003e \u003cli\u003ediscrete algebra theorization limitations\u003c\/li\u003e \u003cli\u003ephysics-based isotropic Reynolds stress tensor modeling \u003c\/li\u003e \u003cli\u003eweak linear algebra admitted non-convergence\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003ethat persist to \u003cem\u003ecompromise\u003c\/em\u003e physics of fluids prediction \u003cem\u003efidelity\u003c\/em\u003e.  Weak formulation \u003cem\u003econtinuous \u003c\/em\u003eGalerkin finite element (FE) basis theorization identifies cubically nonlinear continuum calculus tensor product functionals that totally \u003cem\u003eeliminate\u003c\/em\u003e the need for code \u003cem\u003ephake physics\u003c\/em\u003e stabilization. also stabilized shock capture.   Resultant is classic tri-diagonal stencil equivalent\u003cem\u003e \u003c\/em\u003egeneration of strictly \u003cstrong\u003e\u003cem\u003emonotone\u003c\/em\u003e \u003c\/strong\u003ediscrete approximations that are 4\u003csup\u003eth\u003c\/sup\u003e order accurate in physical space, wave number space and implicit time on \u003cstrong\u003e\u003cem\u003eany\u003c\/em\u003e\u003c\/strong\u003e mesh.  Summarily, matrix differential calculus identifies all nonlinear contributions to the \u003cstrong\u003e\u003cem\u003equadratic\u003c\/em\u003e\u003c\/strong\u003e convergent Newton iteration algorithm to eliminate generation of non-converged solutions.\u003c\/p\u003e \u003cul\u003e \u003cli\u003ecovers incompressible\/compressible laminar, turbulent, transitional thermal-fluid dynamics processes in multiply connected domains with shocks, contact surfaces\u003c\/li\u003e \u003cli\u003erigorous theory derived asymptotic convergence, local and global error estimates, error quantification, stopping criterion for regular solution adapted nonuniform mesh refinement “on-the-fly” code execution at the \u003cstrong\u003e\u003cem\u003eoptimal\u003c\/em\u003e \u003cem\u003emesh \u003c\/em\u003e\u003c\/strong\u003esolution \u003c\/li\u003e \u003cli\u003e mathematical complexity of TEA theory  \u003cem\u003eunstagnation\u003c\/em\u003e advancements are keyed to ready alteration of current practice finite volume commercial\/government and FE CFD codes \u003c\/li\u003e \u003c\/ul\u003e","brand":"A. J. Baker","offers":[{"title":"Default Title","offer_id":48267995119867,"sku":"9783119147767","price":153.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0779\/3917\/9771\/files\/CoreSourceHub_a953307f-36a0-44bb-a2bb-9ac0bdb7362d.jpg?v=1775694183","url":"https:\/\/indiepubs.com\/products\/error-freed-cfd-mathematics-9783119147767","provider":"IndiePubs","version":"1.0","type":"link"}