Refresh HTML Report View During A Build

I am using HTML Publisher Plugin to display test results report as HTML. the tests run-time is about 4 hours and the HTML report is been updated with the tests results during running.

I have the first part of test results after an hour and I want to display it immediately. After I get the other parts of the report I want to refresh the report view during running.

When I run both tasks in parallel I get a new tab to a new report for each time I run the publisher command when I wanted just to update the existing report view.

Any idea how to solve it?

def runRegressionTestsInRemoteServer(globals, testMode, pcapsToRun) {
    echo '*** Run-Regression-Tests ***'
    def tasks = [:]

    tasks["Regression-Test"] = {
        stage ('Run-Regression-Test'){
                tests_function()
        }
    }
    tasks["HTML-Publisher"] = {
        stage ('HTML-Report'){
                while (! finishRegressionTests){
                    DownloadHTMLReport()
                    DisplayHTMLReport()
            }
        }
    }

    parallel tasks
}
def DisplayHTMLReport(){
    publishHTML([
            allowMissing: false,
            alwaysLinkToLastBuild: true,
            keepAll: true,
            reportDir: '',
            reportFiles: 'report.html',
            reportName: 'HTML Report',
            reportTitles: ''])
}

the result I get is :