ABSTRACT A three-dimensional (3D) finite element method is proposed for shallow-water equations (... more ABSTRACT A three-dimensional (3D) finite element method is proposed for shallow-water equations (SWE). The method is based on the Raviart-Thomas finite element approximation. A numerical solution for shallow-water flows is developed based on the unsteady Reynolds-averaged Navier-Stokes (RANS) equations. In this work the assumption of hydrostatic pressure is applied. The SWE equations are solved in a given multilayered system (which consists of an a priori subdivision of the vertical direction of the domain into layers of fixed thickness), with a semi-implicit time stepping method. The eddy viscosity is calculated usind the standard k-epsilon turbulence model. The boundary conditions at the bed are based on the equilibrium assumption of the production terms with vertical diffusion terms using wall functions. To test the validity of the new algorithm the model is applied to three-dimensional flows for which experimental data and other numerical results are available for comparison.
International Journal for Numerical Methods in Biomedical Engineering
Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the solut... more Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient‐specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio‐temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high‐performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning‐based operator approximation, which we refer to as Deep‐HyROMnet technique. Our strategy combines a projection‐ba...
ABSTRACT A three-dimensional (3D) finite element method is proposed for shallow-water equations (... more ABSTRACT A three-dimensional (3D) finite element method is proposed for shallow-water equations (SWE). The method is based on the Raviart-Thomas finite element approximation. A numerical solution for shallow-water flows is developed based on the unsteady Reynolds-averaged Navier-Stokes (RANS) equations. In this work the assumption of hydrostatic pressure is applied. The SWE equations are solved in a given multilayered system (which consists of an a priori subdivision of the vertical direction of the domain into layers of fixed thickness), with a semi-implicit time stepping method. The eddy viscosity is calculated usind the standard k-epsilon turbulence model. The boundary conditions at the bed are based on the equilibrium assumption of the production terms with vertical diffusion terms using wall functions. To test the validity of the new algorithm the model is applied to three-dimensional flows for which experimental data and other numerical results are available for comparison.
International Journal for Numerical Methods in Biomedical Engineering
Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the solut... more Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient‐specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio‐temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high‐performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning‐based operator approximation, which we refer to as Deep‐HyROMnet technique. Our strategy combines a projection‐ba...
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