sustainability Article The Numerical Diffusion Effect on the CFD Simulation Accuracy of Velocity and Temperature Field for the Application of Sustainable Architecture Methodology Vladimíra Michalcová 1 and Kamila Kotrasová 2,* 1 Department of Structural Mechanics, Faculty of Civil Engineering, VSB—Technical University of Ostrava, Ludvíka Podéštˇe1875/17, 708 33 Ostrava-Poruba, Czech Republic; [email protected] 2 Institute of Structural Engineering, Faculty of Civil Engineering, The Technical University of Košice, Vysokoškolská 4, 042 00 Košice, Slovakia * Correspondence: [email protected] Received: 9 November 2020; Accepted: 3 December 2020; Published: 5 December 2020 Abstract: Numerical simulation of fluid flow and heat or mass transfer phenomenon requires numerical solution of Navier–Stokes and energy-conservation equations, together with the continuity equation. The basic problem of solving general transport equations by the Finite Volume Method (FVM) is the exact calculation of the transport quantity. Numerical or false diffusion is a phenomenon of inserting errors in calculations that threaten the accuracy of the computational solution. The paper compares the physical accuracy of the calculation in the Computational Fluid Dynamics (CFD) code in Ansys Fluent using the offered discretization calculation schemes, methods of solving the gradients of the transport quantity on the cell walls, and the influence of the mesh type. The paper offers possibilities on how to reduce numerical errors. In the calculation area, the sharp boundary of two areas with different temperatures is created in the flow direction. The three-dimensional (3D) stationary flow of the fictitious gas is simulated using FVM so that only advective transfer, in terms of momentum and heat, arises. The subject of the study is to determine the level of numerical diffusion (temperature field scattering) and to evaluate the values of the transport quantity (temperature), which are outside the range of specified boundary conditions at variously set calculation parameters. Keywords: CFD; discretization scheme; numerical diffusion; transport equation 1. Introduction Aerodynamics deals with the movement of the air and the interaction between airflow and solid objects. Aerodynamics of buildings study the physical problems of airflow effects on buildings and their surroundings. The motion of the air—the wind—affects not only the design of the load-bearing parts of the building structures, but the dimensioning and construction of their non-load-bearing parts. One of the important areas of sustainable architecture is the knowledge of airflow effects on the surrounding objects [1]. The wind significantly affects the energy efficiency of buildings [2], associated with the general phenomenon of air filtration [3] (see Figure1), the details, elements, and systems of the packaging structures [4]. Sustainability 2020, 12, 10173; doi:10.3390/su122310173 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 10173 2 of 19 Sustainability 2020, 12, x FOR PEER REVIEW 2 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 2 of 18 Figure 1. Illustration of air filtration filtration and numerical simulation [[3].3]. Figure 1. Illustration of air filtration and numerical simulation [3]. TheThe aerodynamics aerodynamics of of a a building building examines the effect effect of the windwind onon thethe structurestructure itselfitself [[5],5], thethe airair velocityvelocityThe near nearaerodynamics the the structure structure of a [6–10] [building6–10] (see examines Figure 22), ),the theth effecte pressurepressure of the on onwind the the structureon structure the structure [ [5,11],5,11], itself thethe turbulenceturbulence [5], the air aroundvelocityaround the thenear building building the structure [12], [12], and and [6–10] the the influence (see influence Figure of of meteorological2), meteorological the pressure conditions conditionson the structure [13]. 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[16 fumes,–18 ]. and the formation of snowdrifts around the buildings and the line transport structures [16–18]. Figure 2. The Computational Fluid Dynamics (CFD) simulationsimulation of the wind around buildings [[10].10]. Figure 2. The Computational Fluid Dynamics (CFD) simulation of the wind around buildings [10]. TheThe results results of of the interaction of air movement and constructionconstruction cancan bebe obtainedobtained fromfrom realreal The results of the interaction of air movement and construction can be obtained from real measurementsmeasurements [19], [19], from from building building scale scale models models in the wind tunnel [[20–22],20–22], asas wellwell asas byby usingusing measurements [19], from building scale models in the wind tunnel [20–22], as well as by using computercomputer simulations. simulations. Computational Computational Fluid Fluid Dynamics Dynamics (CFD), (CFD), also also called called CFD CFD flow flow analysis, analysis, is isone one of computer simulations. Computational Fluid Dynamics (CFD), also called CFD flow analysis, is one of theof thebasic basic methods methods in innumerical numerical modeling modeling concerning concerning fluid fluid flow, flow, and and it it is is used as aa solutionsolution toto the basic methods in numerical modeling concerning fluid flow, and it is used as a solution to engineeringengineering problems problems in in almost almost all all industries industries [2 [233,24],,24], especially especially in in building building construction [4,10]. [4,10]. engineering problems in almost all industries [23,24], especially in building construction [4,10]. TheThe numerical numerical solution solution of of the general transport equations in thethe AnsysAnsys FluentFluent softwaresoftware byby thethe The numerical solution of the general transport equations in the Ansys Fluent software by the FiniteFinite Volume MethodMethod (FVM) (FVM) uses uses the the discretization discretization process, process, in which in which the basic the problem basic problem is the accurate is the Finite Volume Method (FVM) uses the discretization process, in which the basic problem is the accuratecalculation calculation of the transport of the transport quantity throughquantity thethrough walls the of the walls particular of the volumeparticular and volume its advective and its accurate calculation of the transport quantity through the walls of the particular volume and its advectiveflow across flow these across boundaries these boundaries [25]. When [25]. calculating, When calculating, it is necessary it tois countnecessary with to the count occurrence with the of advective flow across these boundaries [25]. When calculating, it is necessary to count with the occurrencethe so-called of “numericalthe so-called di “numericalffusion”, often diffusion”, referred often to in referred literature to asin “diliteratureffusion as error” “diffusion or “numerical error” or occurrence of the so-called “numerical diffusion”, often referred to in literature as “diffusion error” or “numericalviscosity” [ 26viscosity”], and with [26], the and occurrence with the of occurrence values that of are values outside that the are range outside of the the correct range of solution the correct [27]. “numerical viscosity” [26], and with the occurrence of values that are outside the range of the correct solutionThis non-physical [27]. This non-physical CFD artifact impairsCFD artifact the accuracy impairs ofthe the accuracy discrete of solutions the discrete of the solutions equations of the in solution [27]. This non-physical CFD artifact impairs the accuracy of the discrete solutions of the equationsdescribing in the describing advection the transport advection of the transport scalar [ 28of]. the It is scalar known [28]. that It the is numericalknown that di fftheusion numerical occurs equations in describing the advection transport of the scalar [28]. It is known that the numerical diffusionmainly in occurs the case mainly where in the the flow case directionwhere the is flow not parallel direction to is the not grid parallel walls to [29 the]. grid walls [29]. diffusion occurs mainly in the case where the